Bigger picture: what is the underlying problem? If you're having stability problems (wild guess), perhaps your older power supply (wild guess #2) is simply wilting under the load of five drives, five add-in cards and a 1.2GHz Thunderbird. What brand and model does the power supply's label say it is?
example of what I'm after, this is visible when the computer's case is open.
Also, could you nail down what model of Radeon you have, because if it's a 3.3-volt AGP card, you won't want to try to use it in a late-model motherboard. That would be one of the K7S5A's strong points (accepts 3.3V cards), although you could alternately get a new motherboard that has onboard video and do an end-run around the 3.3-volt AGP issue that way.
What I bought for my mom was a Shuttle MN31N, which is an nForce2 board with an integrated GeForce4MX AGP video adapter plus an AGP slot for expansion. It also features integrated Firewire, USB 2.0, NIC, and the fancy nVidia audio processors as well. The only add-in card needed for Mom's rig was a 56k modem.

It performs pretty well considering it's running just a 1.0GHz Duron. You would probably need a new power supply to accompany it, since it'll need a power supply with an ATX12V plug (
photo), and I'd suggest an Antec SL350, Enermax 365-series, or Fortron 350W unit since they have good reputations. And since this board uses DDR memory, you'd need to invest in some of that as well, probably PC2700 so you are ready for future upgrades if needed.
If you do get an MN31N, I guess I should add that it's going to work well with Win2000 and WinXP, but might be finicky about Win98 or WinME. And for Win2000 or WinXP, I'd suggest 256MB or 384MB respectively as the beginning of the sweet spot for light usage patterns (and some of the memory will be used by the onboard video, you can set that to suit your purposes, up to 128MB maximum).