New-to-me iMac with display and boot issues.

This machine sat unused for about a year. The previous user had "tried to fix it", but I have no idea what he did or what problems he was trying to fix.

My experience; First boot got to a login screen and there was obviously something wrong with the display. It's hard to describe, but the splash screen showed random flickers and the color/contrast was obviously off. I didn't have the keyboard handy, so only the mouse (from another PC) was plugged in. I have no passwords, but thought that I could get into the guest account. Unfortunately, the only guest account was "guest1" and password protected. I noticed that the machine is running OS X, though I have no idea which version, as I couldn't log in.

After the first 2-3 boots, the machine seemed to run into more problems. Sometimes, after a soft-reset, the machine wouldn't get to the login screen. Instead, I would see a black screen and after approx. 20 seconds, the fan would go to high speed and the machine appeared stuck. Display problems persisted. After getting an Apple wireless keyboard, I tried "zapping the PRAM"and booting into single-user mode to bypass the login (with varying degrees of success, none of which got me to desktop.) I then resigned myself to fixing the display and boot issues.

Using the guides here, I opened the case to check for obvious hardware issues. Employing the typical precautions, I carefully checked for "bad caps" and LED status lights. LED status showed nothing out of sorts and I could find no "bad caps". I ran fsck from a "command t" prompt and the machine reported HD was ok. In my admittedly ignorant assessment, the computer seems physically healthy.

What can I try next?

Thanks in advance.