Doors Won't Unlock With Fob And Car Won't Start

I've been having problems with my car starting for the last month. I live in West Virginia, and it gets extremely cold there. So, I've had to have my car jumped on several occasions. Recently, I had my car serviced at the dealer. They stated they had tested the battery and it was fine. They stated that it could be because I wasn't driving the car enough to keep the battery charged. A few weeks later after having the car serviced and the battery tested, I try to open my car doors and nothing. I have the batteries replaced in two FOBs, and neither of them opened the doors or trunk. As a result, I researched on how to open the doors manually. I was successful in one of the doors to open, but when I tried to start the car it was completely dead. No lights, sounds or any sign of life in the battery or car. What could possibly be happening. Thanks.