Denied boarding compensation does not apply in this case. I know...I know... they didn't let you board, so the same rules must apply. But they don't as this flight was cancelled for mechanical reasons.

The section you were reading from says you are eligible for denied boarding compensation unless you were denied boarding for one of the following reasons..... one of which is if you're flight is canceled.

If you read the AA Customer Service Plan section on Delays, Cancellations and Diversion Events, you will find some more details there. The "gist" of it is that if you are stuck somewhere away from home and the flight cancels due to something AA can control (mechanicals, crew, etc), they will put you on the next available flight with seats and provide "reasonable overnight accommodations, subject to availability." A further review of the Conditions of Carriage section on the same subject shows language that is essentially identical.

I don't have any experience with hotels.com. I'm assuming you book the hotel through them and pay for the whole thing up front? I'm also guessing that much like priceline, you're out of luck if something happens to prevent you from getting the full use of what you paid for. If so, I would do the math on how much I paid per day for the hotel, and write AA a letter explaining what happened and how you were unable to obtain a refund of the portion of your hotel stay that your cancelled flight caused you to miss. As for the cab ride, you can add that to your request if you feel like you should. You might get a voucher for the value of your request or thereabouts that you can use on future travel. I doubt you will receive a check, but I've been wrong before. Based upon some experience with this from the operator's side of the table as well as the regulator's side, what AA is obligated to provide you in the instance of a cancellation or delay for mechanical (read: safety) reasons is somewhat limited. What they will end up doing for customer service and goodwill reasons is another story entirely. Give it a shot and see what happens.

The above is just my opinion, and we all know that opinions vary.