This is a question about what happens during the "resurrection of the dead". That term is used in both the Bible and the Apostles' Creed (which the vast majority of Christians accept) and discusses how people will be brought back to life when Christ comes again.
The Bible does not go into a great deal about human anatomy (the word "brain" never appears), so we don't have a verse specifically answering your question. The most detailed description of the resurrection of the dead is Paul's explanation in 1 Corinthians 15:35-54. Of note is verses 42-44 (NIV):
So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; it is sown a natural body, it is raised a spiritual body. If there is a natural body, there is also a spiritual body.
There are two main interpretations of this and other Bible passages that deal with it:
- We will be given completely new "spiritual bodies" (with no connection to our earthly bodies) at the resurrection of the dead. This interpretation assumes "dualism": the belief that that our spirit/soul is completely independent of our earthly body and will survive intact no matter how damaged our bodies become.
- Our earthly bodies will be put back together and become improved "spiritual bodies". This may or may not include a belief in dualism.
In both cases, it doesn't matter whether or not your brain and the rest of your body was destroyed in a car accident. Either you will be given a replacement body or your original body will be reformed. If you were impaired due to an ailment such as Alzheimer's disease, then your improved body would presumably not have that and you would be unhindered.
(Wikipedia has an excellent summary of differing views between different denominations and theologians over time, including several points about the resurrection of the dead that are beyond the scope of this question such as whether we immediately gain spiritual bodies in heaven or whether that will happen to everyone at once in the future).