Does Mirror’s Edge run on Windows 7 Home Professional 64-Bit

Run the DSVideoConfig.exe in the installation directory, and explicitly select your video card (rather than the default "Primary Display Driver - Hardware" or "TnL").

Also, it looks like an additional step is needed for Legend of Aranna to work. Copy the first line from the DungeonSiege.ini file in the Dungeon Siege folder to the DungeonSiege.ini file in the LoA folder.

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Your temps are mostly fine, maybe the CPU is a bit hot, if these are idle temperatures.

Seems like it's the RAM or the CPU. GPU faults don't act up like that.

So, you setup an isolated stress test for each suspect.

RAM:
Download memtest86+ and install it on a medium and boot your system with it. I'd suggest USB key:
http://www.memtest.org/#downiso

If it passes the tests, move on to CPU. If it doesn't, find and remove the faulty RAM stick and repeat the test.

CPU:
Download prime95 and run it, no need to reboot:
http://www.mersenne.org/

It might also be that your CPU is running too hot. In that case, open your case (warranty is lost, if any) and clean the dust off from the heat sink and the fans, if any. See if the temperatures drop. If not, the heat sink might have come loose, or has not enough contact to the CPU die. You might want to re-apply the heat conducting fluid.