In LW tools > options > downloads. Make sure that your maximum downloads aren't set at zero.

Otherwise, delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

If that doesn't help, make sure that you're giving LW some time to settle down after starting up (10 mins or so) & also make sure that you're not trying to download too many files at once.