It's got me stumped. Unless we go thru your settings. Your LW 'hanging' is not a good sign. (I suppose you could update to Java 1.5 It's been good for some but others not.) In your LW settings: Tools>Options>Speed do you have Ultrapeer option or have you ticked it to disable UP? Do you wish to act as a UP?
A piece of advice, don't use the Resume button on too many files in a session. If yu apply it to too many, your files will queue for much longer & it may affect LW's connection quality.
Also see some hints on optimising LW:
A well set-up LW can start to automatically continue its dwnlding after it's settled down perhaps 2 out of 3 times you open LW. Optimising LW & Maximising Uplds & Dwnlds A (1st post only) & also Part B which is even better & last & least are search & dwnld hints. The latter one I've been thinking about re-writing for some time. That's just for playing it safe. eg- I show all speeds & qualities.