McGuire Buick Pontiac GMC

I purchased a used 2005 Cadillac Deville on Friday, November 23. The vehicle broke down and died by 10:00 p.m. Saturday evening when my wife attempted to use it for work. The battery was dead and required replacement on Sunday, November 25. The cost for replacement was $175. The battery inserted and sold with the car was not the correct one, and was much too small for this vehicle according to the auto parts store. This explains why the car needed to be jumped several times before we test road it at the dealership. I was told it wouldn’t start immediately because it had been sitting for an extended period of time. That was not the issue or case at all. The car’s original battery had been removed and placed with a smaller inferior one. 
Despite repeated calls and e-mails to our salesman and the sales manager who handled all the paperwork to rectify the situation, it still hasn’t been addressed. I was told it would be handled within 24 hours once the service manager was contacted and questioned. The dealership won’t return any further calls or messages. The sales manager Vinny refused to come to the phone to further discuss the problem and had one of his salesmen tell me there was they nothing they could do and he was too busy. The second issue is false advertising on the same vehicle. It wasn’t until we discovered smoke and burning runoff on the engine that we were told that the engine had been replaced, and the original was blown upon receiving the vehicle. This was not mentioned or indicated in the car dealership's ad. We decided to take the chance on the replacement engine when the sales manager agreed to give us a 1-year warranty on the replaced engine. He would not, however, disclose how many miles this replacement engine had. 
A simple $175 check for the replaced battery would have made me a happy customer. I completely understand there's going to be problems when buying a used vehicle as is, but to have the car die 24 hours later is completely unacceptable.