This iMac (24-inch Mid-2007) has a bad hard drive and a bad SATA/DC/Inverter cable. The hard drive appears to be failing (I/O errors in the log), but doesn't fail SMART - I ran a surface scan, watched the time increase significantly, and determined that it requires the cable too.
Haven't done it yet. Brought it to the Apple store, they took a while to diagnose the bad HD, but refused to replace the cable. As a certified tech that's worked in the field for years (and seen this issue before), I'm disappointed they couldn't even use my diagnosis to reach their own conclusion - it took them days to determine reinstalling the OS wouldn't fix the problem.
It's an awful repair, I wouldn't recommend it to anyone. It really helps to take a picture before removing the cable, as you've got to put the new one in almost exactly in the same place. If you align the cable wrong, there's a good chance you'll need to remove parts to align it again.