annox -- the proxy service someone mentioned on another thread -- that would probably help you get p2p file sharing programs working. Your ISP's filters wouldn't be able to make sense of the encrypted traffic and would pass it along unthrottled.
Sounds more like they've throttled p2p file-sharing speeds to really low values instead of blocking. If it's ip PORT-BLOCKING they're using, turn the tables on them and try non-standard ip ports... and if that doesn't work try ip ports 80, 8080, 21, 135-139, 445, and others that have official dedicated tasks that they DARE not block... not if they want to even claim they give 'internet access'.
BTW, 'internet access' is NOT just access to the World Wide Web HTTP://www. .com websites. Any "ISP" that isn't giving access to various legal networks operating over the internet, which practially ALL file-sharing networks ARE, is not giving full internet access. A carefully worded question can even catch them in the lie of the claim.