Why do I perpetually see a grey screen and spinning wheel?

A few months ago my 2004 iMac froze as I was simply shutting down the power and attempting to restart. I was not installing any new O/S.

Today I attempted two things while booting with the O/S recovery disc-1:

(a) I slid the disc in and held down the "C" key while I attempted to power it on. Nothing happened and I continued to see the grey screen and spinning wheel.

(b) I slid the disc inside and held down the "ALT" key while I attempted to power it on. Three icons showed up: (a) Hard Disk; (b) Recovery Disc; and (c) Test. I clicked on the Test icon and it took me to a new screen with two options: ( i ) Quick Test and ( ii ) Extended Test. I clicked on Quick Test. The first aspect of the Quick Test (I think it was Airport) went through fine and passed. The second aspect of the Quick Test (Logic Board testing) continued to show "In Progress" for a really long time (about 15 mins.). From that I figured something must have gone wrong with the Logic Board.

Can anyone help me as to what could be done? I appreciate everyone's answer in advance. Thank you.