I have two computers connected to Linksys router which is connected to cable modem. On both computers I do not have any other security related software active except built in Windows firewall. While using peer to peer programs I can not get incoming connections. Is it possible that firewall is blocking incoming connections from router?
It is possible. Disable firewall and see what happens. If this is the problem then you will have to open port on firewall for your peer to peer client. There is, also, UPnP functionality in most peer to peer programs that will do this automatically for you but it is functional only on XP computers. Just to be sure, check forwarded ports on router.