Sorry to hear you're having problems. It sounds like the synther isn't being allowed to talk to the internet. This might be due to a firewall program that is protecting your computer or, if your internet is administrated by someone else (say like an IT department at your workplace) they may have a specific list of programs and sites that they allow to access the internet.
In either case, you just need to let whoever is protecting your computer that Photosynth is not a troublemaker and it's safe to let it talk to the internet. If you could find out what firewall you're using, I might be able to give you step by step directions, but if you have someone tech savvy on hand, just let them know that you need to create an exception for Photosynth.
To make sure that I've diagnosed your problem correctly, you could always disable the firewall temporarily and try Photosynth again. Be sure to reinstate your firewall as soon as you're done, though.