linux troubleshooting help

[Dimitri Chausson <tri2000@gmx.net>]

Hi all,

since about 1 week, I am experiencing system crashes. I tried kernel versions 2.6.15 and 2.6.16 but it occurs in both. I first thougth it was X related (so not a kernel problem), but the machine is not reachable via network. All logs I list below were obtained with a 2.6.15-1-k7 kernel (debian):

1- When booting, contains:
-------- output------------
Stack:...
Call Trace:...
========================
Unable to handle kernel NULL pointer dereference at virtual address 00000006
printing eip:
c01037ba
*pde = 00000000
Recursive die() failure, output supressed
<0> Kernel panic - not syncing: Fatal exception in interrupt
-------- output------------

2- Running on a terminal (no X running):
-------- output------------
CPU 0: Machine Check Exception: 0000000000000004
Bank 1: ......... at ...........
Kernel panic - not syncing: CPU context corrupt
-------- output------------


And there were other similar crashes. It crashes really often (several times a day, while the computer is not running the whole day). 
Since I did not add any hardware, I thought some hardware may be dying... but is there a way to know what ? Until now I ran a memtest86, and I checked the hard disk with smartmontools. Both went well...

I do not know how to proceed now, and I would appreciate any hint or help on how to further isolate the problem,

thanks for your time,

Dimitri 

PS: of course, I can provide you with more details if necessary