are you constantly connecting to the same server? or does this happen with every server. Does this happen with any other application/download?
When i had Win98SE Quake 3 TA would run great but once i upgraded to WinMe its been a pain in the ass, it'll start off fine then after a couple minutes everything gets really really choppy and my ping goes up. Although i think its the server in my case (i haven't tried any other servers so i'm not sure)
BTW, I also have 768/128 DSL