4 connections is a lot for a little 56k modem. 2 or 3 is more acceptable. LimeWire will not connect well if you are doing other things with your bandwidth. For instance, if you are surfing the web and using LimeWire at the same time, LimeWire will be the last priority, and the connections will be dropped when the bandwidth is clogged. Also, uploading or downloading files (with LimeWire or any other program) will eat up most of your bandwidth.

If this is not the case, did you try downloading the alternate version of LimeWire? The link is in the FAQ. I would try that if LimeWire is still not connecting properly. Most people have better success connecting to the network with this version.

Post again if you need more help! :-)