If they continue to not be helpful, file a claim with the credit card you booked with. Make sure you have copies of your bills, correspondance, etc.
I am wondering if this could be a problem with the particular hotel. I have used hotels.com as my primary site for years (they are affiliated with expedia, so sometimes your reservation actually shows up as expedia) and have never had any problem and have gotten lots of free nights. But of course contact hotels.com/expedia about this situation.
I wanted to add something after my post yesterday. Always bring a copy of your reservation (in fact hotels.com reminds me a few days before); on it you will usually find a phone number to call if there are problems. So if the hotel says you don't have a reservation and you have the printout on hand, it should be up to them to contact hotels.com
I tend to use Hotels.com as my backup rewards program - when I'm in a city that doesn't have my preferred hotel, when I'm staying in a boutique hotel like in NYC, or sometimes when travelling abroad. I spent 22 nights in hotels through hotels.com last year (some prepaid, some pay on arrival), and fortunately I haven't had any issues. I second the other user's recommendation to print out your reservations. It will show that you've paid (if prepaid), and provides contact information if there are any concerns.
I hope you issue was resolved!