Radio/tape Cd Player problems of the 2006 Mazda Tribute

My battery began being drained for no apparent reason. I bought a new battery but it didn't solve the problem. When it is cold I have to have my car jumped to start most of the time. I sat in the car listening to the radio for about 15 minutes this summer and then found the battery was dead. The rear wiper stopped working and my back up lights stopped working about a year ago. Also the driver's side door would not unlock with the remote. I did have a remote start installed shortly after I purchased my car and it has been checked out and is not the source of the problem. Although not life threatening is extremely frustrating to have to continually find jumps and help in order to drive my car. Not having back up lights may lead to an accident eventually.