Do you see a brick wall in front of the blue world icon at the bottom of LW? See sample below. I've a suspicion the problem is your BTVoyager.
Are you using the laptop in UPnP mode or manual port forwarding? And which is this one using? Which ports are they set to?

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I have a brickwall in front of the globe sign on my PC. I also have a wall infront of the globe when I connect to LW on my laptop but that connects OK on the BT Voyager.

How do I find out what ports my computers are running on?

Not really. If everyone was firewalled then it would be very difficult to downld files. That's why LW created a firewall detector. You should manually port forward the BT Voyager. But you'll need to choose a different port for each computer that's running LW. For one you can choose port 6346 & for the other perhaps port 64049.
I can't find specific instructions for your model but believe it should be the same or similar to BT Voyager 2100 or 2110. Go here http://www.portforward.com/routers.htm & on left-side of page you'll find the BT Voyager models. Then click on the Voyager 2100 link, look for Limewire on the list, then follow all instructions carefully. It is extremely important you set up a static ip 1st, instructions are on that page. But remember, you should set up a separate port for each Limewire you are running. So that means doing the port forwarding twice. Also make any adjustments to software firewall if necessary to clear that port number.
Here's a direct link to the 2100 model: http://www.portforward.com/english/r...0/Limewire.htm If this is not the similar to yours then look at the other models to choose one that is.