Well, first of all, you say "kayak.com / hotels.com" Which is it? They are two separate companies and you need to know which one you are dealing with.
Kayak.com is a search engine that sends you to other websites to complete your booking. Hotels.com is one of those sites. If Kayak sent you to hotels.com, then hotels.com is the site that did your booking, and they are the ones that you need to deal with.
You can also book hotels directly on Kayak, but for US hotels this is just a white label website for Travelocity. I'm not sure about the setup for Saudi Arabian hotels.
What exactly does your debit card statement say? Does it actually say Kayak?
I also suggest you start e-mailing or sending letters. It's very difficult to hold companies accountable for what they promise you over the phone, since there is no proof.