Ok.. here's the deal:

Intel Celeron 2.66Ghz
1024Mb DDR400 memory
Windows XP pro
Onboard video/lan/sound
Mobo: ASRock P4S61

Allways worked perfectly.. Then the rebooting and systemcrashes started..
I re-installed it completely.. Windows updates and servicepacks installed, latest
drivers installed (except for the videodrivers because i couldn't find them) and
the problem seemed to be fixed. Or not..

When I found and installed the video drivers the system kept coming with
rebooting and crashing at random order at that moment I decided to
turn off the auto-restart option on system crash and got the Blue Screens 'O Death.

These told me I had problems with:
DRIVER_IRQL_NOT_LESS_OR_EQUAL
IRQL_NOT_LESS_OR_EQUAL
PAGE_FAULT_IN_NONPAGED_AREA

I de-installed the video drivers in safe mode and thought it would be fixed, but
it wasn't. Still the system crashes and bluescreens. Then I decided to test the
internal memory with mem-test. When i ran it, it said Loading......... and when
it was done loading the system restarted (me never seeing the mem-test).

Could someone please point me in the right direction, cause i'm getting ready
to throw this computer out the window!

You will need to run memtest with only one stick of ram at a time.

take out all other extra components that you dont need to run the system so you have just a minimum setup (psu, mobo/cpu, 1 ram, 1 hdd, audio/video) and try to see if it work ok. If ok, then start putting in things one by one untill you find the problem.

goto C:\Windows\Minidump and post any (5-6 of them if possible) of the new/recent ones here

Ok.. here are the first 5..

And here are the other 2..

hmmk.. this may take a while to go through all these so sit tight (unless someone else decides to help )

Most of your minidumps point to memory (ram) problems or driver problems.

To solve driver problems just go have a look on the net for your updated drivers for everything, as well as windows update service. Even if you've tried this there's no harm looking twice.

The other one is memory problems. This could be caused by incompatible ram or faulty ram. I read in your previous posts that you have a copy of memtest already? Now you need to open your PC and locate your RAM sticks, and if you have multiples of them take them out untill you only have 1 in the first slot. That way accuracy is increased and you can find the faulting stick.
If you've already done so and it still give you trouble loading memtest i suggest borrowing a stick of ram thats compatible to your motherboard and putting it in there and running memtest, and if thats stable try booting into windows.

First I would like to thank you for you help and efford.

I've tried to run memtest on two different sticks or RAM (first one original, second one new), both of the time mem-test didn't load (it rebooted after loading). I allready suspected that one of the drivers was the source of the problem. When the problems originally started, I've reinstalled my entire computer (including the newest drivers etc.) The only driver i had problems with finding was the driver for the videocart and it seemed to me that after the driver of the videocart (original driver from ASRock) was installed the system seemed even more screwed up.

Questions that arise:
1/ Can it be that the problem would be fixed if I installed a PCI videocart?
2/ The BSOD messages lead me to believe I have a problem with IRQ's..
Did me reloading the default BIOS settings help fix this IRQ issue?

You can try.. it won't hurt either way..
I'm not too familiar with IRQs apart from knowing they're addresses for different hardware, and sometimes changing slots (eg PCI cards to a different slot) fixes it.. but seeing that your video is onboard..

Did you try and used a driver cleaner app before you reinstalled a different video card driver? try booting in safe mode and see if its stable (if it is stable then its software/driver related, if its still BSODing then its most likely hardware)

Open up your PC again, and take a look at the mobo. See if you can see any popped capacitors or burns/irregularities etc... There may be a chance that its your mobo thats causing you the grief.. swap this with a replacement to test after you've tried the video card and safe mode..

Do you have any suggestions about wich program to use? I personally haven't heard about such program so I wouldn't know where to look..
Or if you could point me in the right direction..

I've inspected the motherboard when I've first been starting to have these problems. There doesn't seem to be any (visual) malfunctions to the motherboard.. :S

By the way.. I'm thinking about buying a new computer allready so if it's too much trouble for you helping me out or if you want to buy a f***ed up computer for €.. let me know

you can try this driver cleaner and see if it works.. http://www.majorgeeks.com/download3214.html

Play with my hunch.. replace that motherboard with another one thats compatible with your CPU, after all, ASRock brand is a budget level motherboard as i've heard.. i should know, i have the P4 Combo model and i'm still reeling.. (by the way, your CPU is a Socket 478 i think)