1.Most likely reason for slow web access is the DNS settings on your internal network interface are configured (or have been reconfigured) incorrectly. The Microsoft knowledgebase has extensive articles on configuration and troubleshooting DNS. Start there. Sorry for not providing direct links. I'm on the road this week so my Internet access is sporadic and limited.
2. Starting and stopping services doesn't always (actually, it very often won't) fix errors on a Win2k server. You need to look at what details the log provides and go from there. If you can get and post the specifics, maybe we can help you out.
FYI: Windows server errors seldom occur in isolation. Usually something will cause an error that causes an error that causes the error you're looking at. So you'll need to go back and see if you can find when the red flags began. That gives you your first clue about what might have changed to cause your headaches. Also look at any warnings and errors that come up near and around the one you're looking at. I had a client that thought his Active Directory was screwed up because he saw an AD error. What he didn't notice was there were earlier errors flagged on one of his NIC cards which resulted in a huge number of time sync, DNS, and replication errors. Once the NIC was replaced, the server "healed" itself. I only mention this to make the case for looking at everything in the logfiles when you start troubleshooting.
Just thinking. A device or service failure isn't necessarily a problem. I have one client that is using a document scanning/archiving solution that absolutely requires an oddball proprietary virtual PDF printer be present on the server. It cannot be completely removed even though we don't use it. If it's not installed, the rest of the program flags an error and asks to be reinstalled. As a compromise, we just disabled this virtual printer to prevent it being used. This results in the archive manager throwing a service error everytime it starts up (or the server gets rebooted) since it can't connect the virtual printer. Since it doesn't effect anything we're doing or cause any other problems, we just disregard this particular error message.