Try changing port numbers. Make sure that LW on this computer isn't using the same listening port as LW on the other computer.
Then, delete LW's preferences folder (make sure LW's properly closed before you delete the prefs folder). There are instructions for both in this thread: If LW Will Not Connect

Also, try removing the LW rules from Norton's firewall & adding them again. Check out this link: http://www.gnutellaforums.com/226610-post6.html

Since you can use LW on one of your computers, hopefully changing ports etc will do the trick!
TalkTalk are known for causing problems for LW users. If you use the forum search to look for TalkTalk, you'll find quite a few threads

Otherwise, try the rest of the fixes in the 'If LW Nill Not Connect' thread.

If you're still stuck, try enabling UPnP in the router (have a look at the router's manual & there should be instructions). Then in LW go tools > options > advanced > firewall config. Use the UPnP option > apply > ok. Restart LW & see if it connects.

If nothing's working, post back & I'll give you instructions for port forwarding.