Electrical Issues with 2005 Malibu

This issue with my wife's car started with the electrical system. The battery would lose its charge after several minutes things that would cause a minor drain on the battery such as leaving the door open or my daughters watching the DVD player while it was plugged into the cigarette lighter with the car off. It eventually escalated to where we need to jump the car almost every single time we start it. The locks on the car started going haywire and locking and unlocking on their own. This got so bad that i eventually removed the fuse. Any ideas of what could cause this? Are they related? I have been told that it's the ignition but I don't know how that would cause such a drain on the battery.