Zizu your situation looks a little complicated. Hmm many schools deliberately block p2p sharing nowadays. I suspect that's your issue. I missed that point earlier b/c I thought Fabion answered your post. What you can try is set LW up to use another port. Try the following port no.'s one by one to see if any of them work. Go to LW's menu Tools>Options>Advanced>Firewalls & change the listening port from 6346 to another. Try these ones: 3500, 1203, 80, 20282, or 443. You'll need to press the apply button after. Then go to File>Disconnect wait a minute & then File>Connect. Give it at least 15 mins for each one to try to connect.

If that doesn't work, you could try a proxy. But it might also be worth speaking to the systems management people to ask if it's ok to use p2p sharing on the school system & how to achieve this ... are they blocking ports or using a p2p filter program.