Ancient 2008 Mac Pro video card/start up problem

Hello all-

It's ancient I know. I keep my old 2008 Mac Pro around to run some legacy programs I need to occasionally revisit.

Recently, when I tried to wake it from sleep mode a fan came on and whirred constantly. There was no other activity. I shut it down and tried to restart. The fan again came on and stayed on but there was no chime and no further activity. I powered it down, unplugged it and let it sit for 24 hours. After that period was up I powered up the machine. It chimed and it started up perfectly.

Yay thought I. Life is good.

Days went by then yesterday when I again tried to wake it from sleep mode the same thing happened. All fan all the time and no chime. No life. No joy.

I opened it up and reseated the video card and ram modules. I let it sit for an hour and then restarted it with the case open. I then noticed that the fan sound was coming from the video card (ATI Radeon 5770). The RAM cards lights flashed on start up but that was all. Just the fan whirring on the video card and nothing else.

I need get a few more weeks out of this machine if possible. Can anyone suggest a cheap fix? I don't mind replacing the video card or RAM if I have to. EBay to the rescue.

Any thoughts anyone?

Many thanks.