Computer BSODs Within Seconds/minutes, Virtually Unusable?

A few months ago I built my first PC. All parts were brand new, except the graphics card. I couldn't afford the one I wanted so I used an old Radeon HD 4670 - a card that doesn't match the rest of the system in power.Maybe a week ago, I started getting blue screens. At first I'd be able to use the computer for hours before the BSOD. It would generally go by too fast for me to read what it said, though I caught a few error messages, which I will post below. I'd say about 5 days ago is when it became unusable. Sometimes I get a few minutes before it crashed, sometimes only 40 seconds or so. I have been using a family member's (extremely slow) Mac laptop for internet use, and also an iPod touch on the side. Needless to say, I'm beyond frustrated that I can't access any of my music or use a speedy computer to do what I want. I'm worried that I did something wrong while building - but why would it take months to become apparent?

- I ran memtest on the advice of a forum member. Two passes is what they recommended, and no errors popped up.

- I scheduled a check disk, although when I rebooted my computer to let it run, it only took 5-10 minutes - shouldn't it take WAY longer than that?

- System Restore. I tried yesterday and got a BSOD during. Today I was able to restore to the 24th (that was my earliest restore point), however about 2 minutes afterward I got the usual BSOD.

BSOD Errors:It has shown so many errors - it seems to literally be a new one each time. I don't know if I've even seen the same one twice. Sometimes it's on the top, in capital letters, and sometimes on the bottom, with an extension (a file). These are the ones I spotted (especially after I told it not to restart on error so I could read them):

- SYSTEM_SERVICE_EXCEPTION
- IRQL_NOT_LESS_OR_EQUAL
- CACHE_MANAGER
- atikmdag
- cng.sys
- ntfs.sys
- fltmgr.sys
- TDY.sys

Here is my dxdiag, from the 25th.
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System Information
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Time of this report: 7/25/2012, 14:38:50
Machine name: JAMES-PC

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