The test page is a very simple test to find out if you're being blocked from port 6346 which LW uses.
I can't find any info on your modem, other than I end up at a Korean website. Korean is not one of the asian languages I learnt unfortunately. Is it a wireless type connection?
Go to your LW menu Tools>Options>Downlds & make sure you have at least one or more Max Downloads set. Example below. Also go to Tools>Options>Searching>Limit & make sure you have at least 5 set in that option. Press the Apply button if you needed to make any changes.
If this doesn't work, the best I can suggest is to try another version to see if it makes any difference from your personal downld page (if you lost the link you can find it here:
HERE 1st try the Windows(Multilingual) version. Else try:
http://www.oldversion.com/program.php?n=limewire
When you connect it should show coloured bars in the connection quality bar at the bottom left of the main LW window. These should be either green or blue.