Well this is one that I have had something similar to. But there was one Major difference like yours it said I did not have a connection and files were still downloading #5. But I never had the problem of limewire not starting #3. And Limewire worked fine after the connection issue. There is one thing you might try but if you do it you will loose all of you incomplete files.

First move all of the files you want to keep to another folder out of LimeWire. Now uninstall Limewire search your computer for any remnants of limewire IE start/search/files and folders type in Limewire. Delete any files that say limewire.

Now edit your registry IE start/run type in regedit into the run box. Search your registry for anything that says limewire delete it. I do not recommend doing this if you are not sure of what you are doing if you delete something in your registry that you are not supposed to you can mess up your computer.

I see you are running XP before you try any of the above try doing a system restore pick a point before you had a problem with LimeWire. You will have to reinstall the newest version of LimeWire and see what happens.

I have a feeling something has messed up your setting or part of LimeWire has been corrupted some how. I do not know that any of the above will help and it might be advisable to wait and see if any of the other LimeWire members have any Ideas before you try these repairs.