Download and install Service Pack 2. Then install Ad Aware and Spybot. Run both one after the other, to remove most of the spyware on your system. Then download and install AVG Personal Edition. Remove Symantec.
Atleast, this was what I was suggested to do, when I too experienced the same problems in my otherwise-smooth PC. It worked for me!
Ditto on the AVG. I was running Zonealarm also for a while, but it seemed to conflict. W2KSP4 here.
Even with protection, it's handy to use the netstat command often. I did once find a virus using netstat that AVG missed!