Download a file from here (any one) & see what speeds you get. If the magnetmix file downloads slowly, it can point to an ISP shaping bandwidth.

You could try deleting 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.

Just try changing your Java version, some people have had weird problems with that 1.6.0_01. Try this latest update instead (works fine with my LW), use the JRE offline installer & remove your current LW version(s) before you install this one.
Java SE Downloads

If that Java's no good, try this older update. Same deal with using the JRE & removing old Java versions before reinstalling.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Try changing ports. In LW tools > options > advanced > firewall config. Change LW's listening port to 64049 (or something in the range of 49152 - 65535) > apply ok.