Have you ever been able to connect with p2p apps? Do you know if any other people in the complex can use p2p without a problem? Please give us your details.
System details - help us to help you (click here)

Try changing ports. In LW tools > options > advanced > firewall config. change LW's listening port to 64049 > apply > ok. You can also try other ports in the range of 49152 - 65535.

Do you know which ISP the block uses? There could be a firewall associated with the block's internet setup...talk to whoever's in charge of the internet there & see if they can help you out