I just downloaded limewire last night and it was working fine. This morning I tried to use it and it will not connect. I am connected to the internet with a 56K modem and am currently getting 50000kbs.

Neither can I. Limewire seems to be a crapshoot. Sometimes you can connect, most of the time you can't.

There's not much you can do if your connections are being refused, but some people have better success by sharing more files (~100), opening port 6346 in a firewall , and setting up the router (if one is used) to help others connect. You can find most of these suggestions in the Tip of The Day and the User Manual in the LW Help Menu. I read somewhere that running a couple of hours each day also gets you recognized as a reliable host.

I just checked my stats--I was able to accept 1,200 connections this weekend, but 25,000 were rejected, mostly because all the slots were filled. As the network gets more people willing to run as ultrapeers (accepting incoming connections) and people willing to share, connections will be easier for everyone.

I've got about 55 files I'm sharing, and am on around 4 hours at a time every day. When I can connect, I can usually download pretty quickly. Did about 5 in less than an hour last night. Tonight, nothing. Checked firewalls, port, etc, everything is fine. I still think it is just that sometimes you will connect, sometimes you won't .

Sounds like you're doing everything right, so I'd think you should connect. Especially if you see some uploads. What version of LW are you using, and how do you connect to the internet?