I have had a few SE's have that icon, and it usually means the HDD is dead. Swapping it right out with a known working drive fixes it. People don't tend to swap a good HDD into a machine and then not install system software, so it normally indicates a bad drive.

Sounds as though you may also have logic board issues as well. The caps in these tend to crap out far more than the older boards in the SE and earlier models.