Oops: Unable to handle kernel NULL pointer dereference at virtual address 00000004

NULL is address 0, which is never a valid value for a pointer. Basically, the kernel has tried to access whatever is at address 0, which is an invalid operation, and so it's killed itself (to prevent it from doing any more serious harm).

One possible explanation for this is a (physical) memory error, typically caused by a damaged RAM chip. Another possibility is a motherboard bug from a few years ago, where some BIOSes would report a memory SIMM (DIMM?) as having around twice its actual size; attempting to access the area above the first half would simply return 0 (hence lots of NULL pointer  errors ). If this is the case they you can try the mem= bytes  kernel command-line option to tell your kernel how much RAM you actually have.

I can guarentee you that if a memory bug existed in the paging code (which is where your kernel was when it crashed) then it would have been fixed by now. I can only assume that you've tried upgrading to the latest kernel release for Fedora.

One test you can do to see if your memory is working is to download the source code for gcc and compile it (don't bother installing it; just compile it). If it crashes, but then crashes in a different place the next time around (after re-issuing the make command), then you definitely have broken RAM.