You haven't given very many specifics, but if they took your money and didn't provide services as advertised, and then didn't refund your money upon request, you can report them to the Attorney General in the state where their business is located, and to the Federal Trade Commission's Department of Consumer Protection.
Note the following. The BBB does nothing but record complaints against companies, and make those records available to the public. They can take no action except to act as an intermediary between you and the company with which you are having a problem. Honest companies will generally respond quickly to a BBB complaint, dishonest companies will not. But *NO* company wants complaints on record with the AG's office as a number of complaints can lead to an investigation by the AG.
If the dollar amount is large enough and you have a winnable case (check the company's TOS for sure), file a suit against them. If they are unresponsive, you'll win by default. You can then have that judgement entered in their D&B credit file or the owner's personal credit file if they aren't incorporated. This will force them to deal with you because you'll cut off their access to credit, which can be a very painful situation.
When they're ready to deal, offer to have the judgement removed from their credit file if they deal with your complaint.
A good company would never let it get as far as court, though, so be sure to give them 10 days notice that you will be taking them to court (via signature requested delivery) so they'll have one last time to deal before you spend your money on court filing fees.