I've got OSX 10.2.6 and Limewire 3.5.8...have cable internet using a Motorola Surfboard cable modem.

Here's the problem...if I'm running limewire and then quit, it disconnects me from the main internet server and I have to restart both my computer and my modem to get back online. Tested it today and my connection went as soon as I 'quit' LW.

Try waiting for two minutes or more before restarting--service should resume. A couple of other ways to help ease the transition--use file->disconnect a few minutes before quitting (uploads and downloads will still continue), and you can also quit all Internet apps to help.
Especially if you were running as an ultapeer, some cablemodems and the OS can take a while to terminate all the interrupted threads--which seems like a freeze. (my ISP eventually provided a DOCSIS cablemodem that doesn't "freeze" on me anymore).