The Fourth Gospel plays an important role in determining the probability of the claim that Jesus died on the cross.

Two of the key injuries allegedly inflicted upon Jesus are documented only in the Fourth Gospel:

1. Jesus’ hands and feet were nailed to the cross.

2. Jesus was stabbed in the chest with a spear while on the cross.
None of the Gospels state that Jesus was nailed to the cross when they describe the crucifixion. They just say that Jesus was crucified. Crucifixion does not necessarily involve nailing the victim to a cross. It only requires that the victim be attached somehow to a tree or a stake or a cross.

Only the Fourth Gospel specifically mentions nails in relation to the crucifixion, and the reference occurs not in the crucifixion scenes but in the resurrection scenes where Jesus allegedly appears to his disciples in Jerusalem after the crucifixion.

So, if the Fourth Gospel is historically unreliable in relation to the details of the crucifixion and the details of the post-crucifixion appearances of Jesus, then the case for the death of Jesus on the cross is significantly weaker than most Christian believers and Christian apologists think it is.

According to the scholars of the Jesus Seminar, the Fourth Gospel is very unreliable, and there are very few details in this Gospel that are historically true or even probable. The scholars of the Jesus seminar color John 19:26-37 black, meaning: “This information is improbable. It does not fit verifiable evidence; it is largely or entirely fictive.” (The Acts of Jesus, p.37).

The concluding comment on this passage is clear:

Aside from the notice that some of the women were present at the crucifixion in v.25, the Johannine version of Jesus’ death, like other gospel versions, is the product of imagination laced with scriptural allusions. Black is the correct color. (The Acts of Jesus, p. 439).

So, according to the scholars of the Jesus Seminar, the spear-wound incident in the Fourth Gospel is probably fictional rather than historical.

A similar negative verdict is given on the Doubting Thomas story in the Fourth Gospel, which contains the only specific reference to nails in any of the Gospels. John 20:19-29 is colored black by the Jesus Seminar scholars:

Although claims have been made for the Thomas story as an independent tradition, the Fellows were inclined to regard it as a late and fictional tale. (The Acts of Jesus, p.488).

Thus, in the judgment of the Jesus Seminar the passages of the Fourth Gospel that provide important details about the crucifixion that, if true, would make the death of Jesus on the cross probable, are themselves probably fictional. If we follow the conclusions of the Jesus Seminar, then the details and stories of the Fourth Gospel are generally dubious, and the specific passages in the Fourth Gospel that support the above two key claims in support of view that Jesus died on the cross should be rejected as unhistorical.

However, Evangelical Christians and conservative Catholics tend to have a negative view of the Jesus Seminar scholars as being overly skeptical about the historical reliability of the Gospels.

Many Evangelical and Catholic believers think that the Fourth Gospel was written by John the apostle, who they think was an eyewitness to the crucifixion and to the post-crucifixion appearances of Jesus to his disciples. So, from their point of view, the above mentioned passages from the Fourth Gospel provide us with eyewitness testimony supporting the two key claims about the wounds inflicted upon Jesus.

Many Evangelical NT scholars, unlike most Evangelical Christian believers and most Christian apologists, do not hold the traditional view that John the apostle is the author of the Fourth Gospel.
Evangelical NT scholar Rodney Whitacre tries to break the bad news to naive Evangelical Christians by putting a positive spin on his more skeptical view of the authorship of the Fourth Gospel:

We will dive in at the deep end with some of the most difficult questions. The answers to these questions will not affect our respect for this material [the Fourth Gospel] as inspired scripture, but they will give us an appreciation for the wondrous complexity of its production, very much analogous to God’s working in the realm of nature. (John, The IVP New Testament Commentary Series, p.13-14)

George Beasley-Murray, another Evangelical NT scholar, also gives his readers a bit of a heads up at the beginning of his introduction to the Fourth gospel:

There was a time when the subject indicated by the above title [‘The Origin of the Fourth Gospel’] would have been considered superfluous; for the tradition was unquestioned that the Gospel was composed by the apostle John on the basis of his own memories, with no other assistance than the prompting of his friends and colleagues to set down in writing his recollections of Jesus. The question of authorship, however, is not so simple; the answer has to take into account evidence relating to other sources of information about Jesus and considerations that arise from the book itself.(John, Word Biblical Commentary, Volume 36, 2nd edition, p.xxxv)

In the IVP Dictionary of Jesus and the Gospels, the Evangelical NT scholar M.M. Thompson, opens the section on the authorship of the Fourth gospel with objections to the traditional view of the authorship of this gospel:

The Gospel itself comes to us anonymously, as do all the Gospels and, in fact, much ancient literature. The title ‘According to John’…is derived from the tradition that the Gospel was written by the apostle John, the son of Zebedee. This tradition has been challenged for the following reasons: (1) The evidence of the earliest sources and church fathers…is deemed ambiguous, inadequate, wrong, legendary or polemical. (2) Those statements within the Gospel which might allude to its authorship…are also ambiguous and perhaps even point away from authorship by one of the Twelve. (3) The content of the Gospel suggests that it was not written by an eyewitness or by one of the twelve disciples of Jesus.
(‘John, Gospel of’, IVP Dictionary of Jesus and the Gospels, p.369)

After reviewing the relevant evidence, Thompson suggests a fairly skeptical conclusion on the authorship of the Fourth gospel:

A common understanding of the Beloved Disciple is that he is a person who heard and followed Jesus, although he was not one of the Twelve. That there clearly were such persons is obvious from the rest of the NT (Acts 1:21-26). He exercised a role of leadership in one group of early Christian congregations, probably gathering a circle of disciples around him. One (or more) of his disciples wrote the Gospel, but who this author is remains unknown to us. He preserved, shaped and interpreted the witness of his master, the Beloved Disciple, who had in turn interpreted the teaching of the Master himself. (IVP Dictionary of Jesus and the Gospels, p.370).

Rodney Whitacre rightly shows respect for the views of the great Catholic NT scholar Raymond Brown concerning the authorship and composition/revision history of the Fourth Gospel (see John, IVP NT Commentary, p. 14-27).

Brown initially argued that John the apostle was the ultimate source behind the Fourth Gospel, but that the Gospel went through five stages of development and revision, thus allowing for a good deal of additions and alterations of the original oral traditions/sources. Whitacre notes that Brown later concluded that ‘the Beloved Disciple’ the original source behind this gospel, was not John the apostle. In Brown’s view, the Beloved Disciple was an eyewitness, but was not John the apostle, and was not the author of the Fourth Gospel. The evangelist or author, in Brown’s view, was a prominent preacher in the Johannine community, who used traditions from the Beloved Disciple to formulate his own sermons which he also wrote down, and this document went through editing and revisions, including a final revision that was done by someone other than the evangelist.

Whitacre settles on a more conservative view than Brown, but still does not fully support the naive traditional view:

I will refer to John as the author not in the sense that he necessarily wrote it all as it stands, but in recognition that it is his witness that is presented here and that he at least caused it to be written (21:24). (John, p. 21)

Beasley-Murray, on the other hand, opts for a more thoroughly skeptical view of the authorship of the Fourth gospel:

The Beloved Disciple is not a member of the Twelve, nor a well-known person in the early Church.

The Beloved Disciple is not the author of the Gospel-neither of chaps. 1-20 nor of chap. 21.

He [the Beloved Disciple] is the prime source of the traditions about Jesus in the Johannine circle.

As with the Beloved Disciple, so with the Evangelist [the author of the Gospel]: we do not know his name.(John, Word Biblical Commentary, Vol. 36, p. lxxiii-lxxiv)

There are, of course, Evangelical NT scholars who still support the traditional view that the apostle John wrote the Fourth Gospel, but skepticism about the traditional view is not limited to the liberal scholars of the Jesus Seminar. Many prominent Evangelical NT scholars also question and sometimes outright reject the traditional view of the author and composition of the Fourth gospel.