Intermittent Internet Access

I have just installed SP3 on my Windows 2000 server, set with AD and a domain. This server is on a network connected to the internet via a cisco router. I have had absolutely no problems until after I installed SP3. My IE browser can find the internet most of the time, but randomly (and now frequently)can not open or display a website. Email also fails, as well as a ping to an external DNS server. I have the DNS set for forwarders, and use this server as the DNS server for my clients. Has anyone heard of SP3 causing this problem? How can I trace what is going on with DNS to see what the problem is? Could something else be the cause?