Possible causes for memory failure and crashes, with any RAM boards?
My niece's iMac 7,1 (Mid 2007, 20 Inch, 2.0 GHz) is crashing and freezing, usually soon or immediately after startup. Sometimes it fails to get past the black screen at startup, and plays error beep sequences. At first these error beep sequences were short-short-short-short-long-short-long, which I haven't found documented anywhere, but all later error beep sequences were different: short-short-short-long-long-long-short-short-short, which is Morse code for SOS. Occasionally the Mac will run for 15-20 minutes, but not often; when it does, it often finally displays a kernel panic screen. The first test we did was to run the Apple Hardware Test CD (on this occasion, the Mac ran long enough to let us do this), but it didn't find any problems. Next, we tried different RAM boards (both in pairs and singly), including two new RAM boards, but that didn't help. Even though the problem didn't seem to be due to bad RAM, I ran the Memtest utility by Tony Scaminaci anyway, to see if the RAM controller circuitry might be bad. Memtest showed memory errors almost immediately (I tested several times with the same result). I also disconnected the internal hard drive, and tried to start up from an external drive, but that didn't help. Since these problems often occur immediately after powerup, it's unlikely they're due to overheating.
I think the problem is on the logic board, where the RAM controller circuitry is located. Does anyone have any other ideas? Could a bad processor (CPU or GPU) cause errors like this?
Edit April 25:
I bought a replacement logic board for this iMac, and I'm in the process of installing it today. Though I know I didn't get any suggestions here for my question, I'd still be interested in hearing some, but iFixit archived my question April 14 because, according to them, I "did not provide enough information to provide an answer." I thought the information I provided was pretty detailed, so I don't know what the "not enough detail" refers to.