Whilst LW is closed try deleting your LW Preferences folder called
.limewire & found here: C:/Documents And Settings/your_username/.limewire
Keep in mind your settings will be deleted also so make a note of them before you delete the LW prefs.
What brand name & model number of modem do you use?
After LW has been open for 20-30+ mins can you do this test for us:
Bug Report instructions & sample image Is your result True/False?