Strangely enough I have another thread posted about problems with my UPC wireless internet, but they have been great to me, both on the phone and sending out technicians.
My advice would be to not self-diagnose the problem, but let them do it. If they can't fix it over the phone (and plugging your computer in directly is not fixing your wireless problem) then they should send out a technician. It's up to the technician to decide what needs to be done, and I think he or she should have some spare equipment in the van and be able to swap your malfunctioning unit for another one, if that is the problem.
I agree that UPC are your service provider, and they should either provide a working service or do whatever it takes to provide a working service. And I also agree that if you're fobbed off again you should ask to speak to a supervisor. As I said, I have found them great as regards investigating problems, maybe you just got a bad person on the phone.