I applied for this visa over a month ago and I still haven't recieved the card. I've made calls to the company only to hear a recording telling me to call back later. I also tried to access them over the internet but the website is down for some unknown reason.

I've already recieved a bill and paid it. Is there anything I can do to get my money back and cancel the card all together?

Is this through a bank or other recognized institution, or just some site you found on the Internet? The fact that you can't contact them and their website has disappeared doesn't sound good - sounds like you've been scammed. And if so, there's probably very little chance of getting your money back - scammers are real hard to track down.