I do not have a good connection. No results are comind out.What might gonna be my problem?

I called my ISP and they block gnutella packets because it was slowing down their DSL servers!! GRRRRRRRRRR At least I know what the problem is now.
Mindy

Pardon? What ISP? And how will I fix it?

Who is your isp? If LW suddenly stopped working 2 weeks ago & Bearshare also refuses to connect, it sounds suspiciously like your ISP is at fault. Options: change isp or try using a proxy. A Fix for those whose ISP's block Limewire pages 1 - 3 which have links to alternative instructions. eg: Tor
You could also try connecting thru a higher port such as between 49152 - 65535. ie: go to LW's menu bar, Tools>Options>Advanced>Firewalls & change ports there.

My problem is simple: I downloaded 4.12.3, and although the old limewire was working great with avast, the installation gets as far as starting to open the program and then says "Limewire was unable to initialize and start. This is usually due to a firewall program blocking Limewire's access to the internet or loopback connections on the local machine. Please allow Limewire access to the internet and restart Limewire."

The thing is, it's not blocked, and my ports are open. I'm not sure what to do with it??