You're not seeing the firewall icon, which means that there's not a problem with your software firewall or with your router. What happens when you try to download something??
Do the files move into the download pane? Do they sit connecting for ages & then get stuck needing sources forever? Do they connect ok but then show 0 KB/s for the download speed?

Sorry, but Talk Talk customers have a lot of problems. Have a look at these threads below. If you use the forum search to look for Talk Talk, you'll probably find more threads

Is that it then, TalkTalk

ISP's known to BLOCK or Filter p2p or specifically Limewire

1-3k downloads

ISPs that throttle p2p - The Scream!

You could try changing ports but there's no guarantee that it's going to help you. In LW tools > options > advanced > firewall config. Change LW's listening port to 64049 (or something in the range of 49152 - 65535) > Apply > ok.