When I play OLDER games or am on the internet the screen sometimes freezes (more often while playing games) and either manages to reset itself or I have to restart the computer. The monitor also occasionally switches itself on standby and I have to restart the computer. I have the latest drivers for the card.
My system specs are-

Abit VA-10 mobo
Athlon XP 2200+
256mb RAM
Radeon 9800 pro
NEC DVD RW
CD drive
Floppy drive
2 hard disks (one 80gb the other 6gb)
300W PSU

First make sure you have updated your gfx card drivers to the latest edition: https://support.ati.com/ics/support/...ge&folderID=27

done that

What kind of old games are you trying to play, e.g DOS based?

It might be worth trying to un-install your video card and then re-install it just incase it is a corrupt driver.

Does the monitor go on stand-by after a period of inactivity or it is while you are doing things?

Older games as in AvP2. I think the monitor goes on standby because of the small PSU though, it's just the screen freezing that's the main worry.

Do you have any old drivers for your video card still on your machine, I have had a problem before such that when I updated the drivers I was unable to play some of my older games.

If you have older drivers try to install them