Don't use 2 software firewalls at once...chances are they'll conflict with each other. Choose the firewall that you want to use, configure it so that it's allowing LW & disable the other firewall

It's not a good sign if the test page won't display, something may be blocking LW's default port. You could try changing ports. In LW go tools > options > advanced > firewall config. Change the listening port to 65000 (or something in the range of 49152 - 65535) > Apply > ok.

Does the appartment complex have a manager/supervisor? You could ask whether the internet connection allows p2p use. Also ask which ISP they're using.

Which version of Java are you using? There are fixes to try in the thread below. But if it's something associated with the appartment's internet setup that's stopping your connection - there might not be too much you can do.
If LW Will Not Connect

You could also try these other p2p apps & see if any of those connect.
Phex
FrostWire
BearShare

If it turns out that it's an ISP problem, have a look at these threads.
ISP's known to BLOCK or Filter p2p or specifically Limewire
Important!!!!!!! A Fix for those whose ISP's block Limewire