Laptop: Try a USB modem or a PCcard modem. Both should work in your laptop. It may just be a driver issue, but modems do go bad.
Desktop: Check the "hosts" file in your computer. Spyware or viruses may have hijacked the addresses of anti-virus and anti-spyware websites to prevent updates.
Look for entrys like
www.symantec.com 127.0.0.1
These make your internet connection look on the local computer for these sites.
Appreciate the info. My big question with the desktop is why with the Spyware Guard update attempt my computer popped up with a box asking me what I wanted to do (I believe it was along the lines of connect, block, etc. like it would for an Active X prompt). After clicking "no", just to be safe, I get the same "can't connect to server" response.
If it's a driver issue, how do I check/repair that?