I am aware some ISP's in South Africa are not friendly to p2p users. Don't know if yours is one of those. Also as Birdy pointed out, it can be a little complicated when trying to connect via an appartment network. Since you have no access to the router, you don't know what type they are using or the settings. There's a chance you are firewalled by the router without UPnP or port forwarding abilities. Which means the default port LW uses is definitely being blocked by something. Either the ISP or the apartment router. BTW did you configure your XP firewall? -> Windows Firewall - LimeWire

Try Birdy's suggestions above. But not only with the listening port, but change setting to Port forward & change Connection port also to one between 49152 - 65535 such as 64049. Some others to try are: 1111, 3500, 4008, 1203, 10000, 15189, 80, 443, 427, 20282, 22817, 34599, 40475, 65530, 6295, 8360, 19515, 20285, 22091, 25079, 26394, 33307, 33049, 42628, 52343, 51002, 50012.