Did Parallels Tools install properly? Check the version in Windows.
It isn't helpful to say you can't connect to the Internet without some additional information. Perhaps you have IP connectivity but your DNS is broken, for example. Try pinging some IP address from a Windows cmd tool. The IP for parallels.com is 64.131.89.6 so try to ping that. If it is successful then your IP stack is in good shape but your DNS is borked.