This sounds like a severe ram or java issue!!! What's the comp model you have? Java version? Ram? Processor Speed? Available Hard Disk Space?

Oh, I only just realised your late edit! See if you know anyone who CAN connect using p2p. Find out the port they're using, try that for lw. Otherside if they use LW see if you can get a copy of their LW prefs (.limewire). Failing that, see if you can make buddy's with the network support person/tech & see if they'll help you. The recent beta is supposed to make it easier to connect thru firewalls.