This really does sound rather like a hardware problem to me, probably a memory problem, could well be a CPU problem.
You can use memtest86 to test the memory, this is something that starts at boot time in place of an operating system and will test the whole memory for errors, it may take some time. You can either start it from lilo (or other boot loader), or you should be able to make it into a boot disk and test it from there.
In any case, random things segfaulting without apparent reason or connection sounds very very much like a hardware problem. Apart from the memory one of the first things I would check is to see if the CPU heatsink/fan is still intact and functioning. Hot CPUs are not happy CPUs
