I'd still try a few things to check.
You say ARES stopped working before you got the router. That's important as we need to see what happened when it first stopped working.
Did the failure coincide with the change of ISP by any chance?
I can't find anything on Google suggesting that your ISP blocks P2P but maybe it's too small a company to show up.
I really don't like what you say about their installation though, Sounds very odd to me.
OK, let's backtrack.
If the problems started exactly with a change of ISP then contact them and ask "do you block P2P programs".
There's nothing illegal with the programs themselves. It's what people DO with them that's the problem so you won't get into trouble for asking them.
If it didn't start with a change of ISP, then we need to look at the setup again.
What's the exact name of your ISP? (ie sitco.com, sit-co.net etc)
There are sometimes problems with ISPs blocking ports (that would allow the Linewire test to work - as it did - but still not connect) but that is a default setting for security and can be changed.
Here's a site to check.
Security Scan
Try this to check (just work your way through the tests). Then check the ports against the ones you use for P2P programs.
Sorry this is so long winded but without actually sitting by your PC we are making "best guesses" and there are hundreds of reasons that this could be happening.
You'll probably find that the answer is something very trivial like an incorrect setting somewhere or a closed port.
Don't give up and keep posting and let us know the results.
DO remember to work your way through the other suggestions made as well like deleting that file etc.
And do things ONE AT A TIME and retest Limewire after each one or you'll never know what it was