BSOD doing random things (Google Chrome, minecraft, random times)

I have finally had it up to here with the BSODs, so I really need help. I ran a windows memtest and it detected no errors. I just finished updating to SP1 with pretty much most updates too. The BSODs I get the most are:

Driver IRQL not less or Equal
System Service Exception

and these two I just got before I decided to post:
Interrupt Exception Not Handled
No More IRP Stack Locations

I recently took this desktop back from my brother. I bought a new harddrive and installed a fresh Windows 7 x64 Home Prem. on it. I have two other HDD's connected too, a 1TB and a 500gb. I built this originally (and I had no problems when I built it) back in 09. System Specs are included. I replaced the RAM too. I know it isn't on the Approved List for my mobo, but nothing on the mobo lists 8GB and I'd like to use 8GB.

My parts are:

Asus P5P43TD Mobo
Core 2 Duo 8400 Wolfdale
(2x4gb GSKILL F3-12800CL9D-8GBRL)
XFX Radeon HD4890 (but i hadn't noticed, but radeon now only sets out drivers for the entire series, 4XXX, etc.)
Sunbeam (Ithink) 780w psu

I'm not in the market to buy a new performance pc (although the parts I have my eye on are roughly 1400)

Please lmk what you think I should do.

I see some memory corruption in the dumps. Can you follow this tutorial: http://www.sevenforums.com/tutorials/105647-ram-test-memtest86.html

Report back after the tests

Thanks Ant

Idk which dump you might have looked at, but I used to get memory management. And I bought two sticks of ram to replace the old ones so those maybe from the original bsods. Hope that might help. And I'm doing memtest now. It's just very long.

I did the memtest. I pretty much got fails with everything. I don't know if it is my sticks (which shouldn't cuz they're new) or my motherboard is just messed up.

Bumping an old thread. I got this computer to the shop and they told me the Graphics Card was not working. But I don't know if they diagnosed it properly because I got memtest fails and I didn't have problems with my graphics card.