It definitely sounds like a network issue, if you are getting the same results on 5 different computers. Spybot doesn't (I don't think) block access to websites, unless they are particularly dubious. It is a spyware scanner, which detects and removes spyware and / or malicious programs, much in the same way as an anti-virus program would. I use it myself, and I can still access Yahoo! Mail. Maybe your network has been set to block certain websites, or this could be a network firewall problem?
Unless anyone else here has any ideas, I would suggest you have a word with your network administrator, to see if any sites have been blocked, and / or you could also try a different browser, such as Firefox, or Mozilla, both of which can be found in my sig, below.