Dial up can be a little sensitive. Don't use the Resume button on all incomplete files. This can have side-fx such as affect LW's connection quality. May queue your files for much much longer. This will also stress LW & your comp. If you use Resume/Find sources then just apply it to one or so at one time. Don't try to downld too many files at one time.

May I ask why you're using 10.3.5 & not later? I guess the updates take a long time on dial up. Can you check the version of Java you're using (go to menu bar, About LimeWire under the Limewire word at top left corner next to the apple icon.

It may be worth deleting your LW preferences file whilst LW is CLOSED & found here: /Users/your_username/Library/Preferences/LimeWire

It's often wise to do that after uprading to pro. But make a note of any settings you have because once you delete this file, the next time you open LW, you'll need to reset the options.