What to do if I booked a hotel room on-line and paid the fee in full, however now they have reneged on the deal saying that the price was a mistake?

You have a valid contract.  A valid contract requires an offer, acceptance and consideration.  An offer is a manifestation of present contractual intent imparting definite and certain terms communicated to you.  This occurred because the offer identifies the parties (you and the hotel), the time for performance (date you are to stay at the hotel), subject matter (room at the hotel), and price to be paid for the room.  Upon your acceptance communicated to the other party, a valid contract was formed.  Consideration is a bargained for exchange of promises; the hotel room in exchange for your payment.  The confirmation e-mails also confirmed the price and provide additional evidence of the validitiy of the contract.  If you did not know and had no reason to know of the mistake in price, the contract is enforceable against the hotel.  If you knew or should have known of the mistake in the price, the hotel would have a defense to enforcement of the contract.

If you did not know and had no reason to know of the mistake in the price, if the hotel does not honor the stated price, you can sue the hotel for breach of contract.  This would be a Small Claims Court case.  Your damages (the amount you are seeking to recover in your lawsuit) would also include consequential damages which are damages flowing from the breach of contract such as having to make alternate accommodations.  You will need to mitigate (minimize) damages) by NOT selecting the most expensive hotel in the area you can find as an alternative, but something that is comparable to what other hotels in the area are charging.  If you were to select the most expensive place you could find, your damages would be reduced accordingly.  Your damages would also include court costs.  Court costs would be the court filing fee and process server fee.