I have a Duron 1300, 512Mb SDRAM, GeForce2MX.
Spring runs just fine (except CA with it's fancy graphics) on 1024*768, graphics near the lowest (I'm talking about normal games, not speed metal with 200+ gunship rushes), less than 5 players (but still you CAN play 3v3, even if it becomes slow after some time) and without gong overboard with widgets (team platters, unit highlight and seeallcommands not recommended).
First I had the problem that after 10-15 minutes, the game was slowed down to a crawl, except when looking very close to the ground. Pretty much everyone was telling me it was my system specs, but I didn't have this problem when I played against the AI through springtest!
Turned out that for some reason the culprit was my router, when I de-activated it, this problem didn't show up anymore! :D
BTW, do you know what ports you have to open for spring and TASclient?
EDIT: It looks like ping is somehow related to your processing power, I tried to play DSD 5vs5 once, and after 30 minutes or so, when the game slowed down to a crawl, I had a ping in thousands of ms!