Non response from tower
If you're hoping for a bargain out of it, it depends how much your time is worth. Given that the PSU was dead, and other components are showing problems, one or more of them were probably affected. Could be the fan is spinning slow due to damage, and the motherboard is refusing to fully init because of the fan... but I doubt it.
The CPU may or may not be okay, but the value is likely to be low. The RAM is probably okay, but again, value is likely to be low. Your best bet would be if you had a second similar computer, to try interchanging parts and see which are damaged/working.
In general, though, the system probably is of very low value when working. It looks like it may be model T3624; if so, a model recently went on eBay for $140 (including shipping), in working condition and with 512mb RAM. (item 190155139483)
Personally, I would try to sell it as-is for $75, with the dead PSU, or the amount you paid for it (if applicable). Depending what the PSU cost you, you could also add that to the price and ask for that, with the working PSU.
At the end of the day, the question becomes, how much would it cost to buy this computer (or a similar model) in known working condition? Is the value of your time, or replacement parts, going to exceed that?