LimeWire, since it implemented Ultrapeers, seems to take its time after starting it until your search horizon has grown to a sensible size. And here I don't mean the figures shown in the statistics window, but you'll have to wait a few minutes until search queries return lots of results. Also sometimes you are connected to Ultrapeers on crappy connections (some clients seem to try uploading two or three files while keeping up ~50 connections with an upstream of 128kbit/s).

Some solutions for you problems might be to wait until you are properly connected (shouldn't take longer than two or three minutes). If it still doesn't work, you might want to set the connections to keep up in the Connections-tab to a higher value (maybe 6 or so). Also check, that you are throttling the bandwidth of your uploads. You should reserve at least 2 or 3 kbytes/s of your upstream for connections only if you are a simple client and at least 12kbytes of your upstream if you are an Ultrapeer.