i just bought a 2006 A4 2.0t avant and it wouldn’t start the very next day after the purchase. Brought it into a shop: battery is good, alternator is good, fuel pump is good, starter is good. They identified a drain coming from the head unit (radio) so they unplugged the head unit’s fuse and that resolved the problem. Shop suspected a faulty head unit harness. The Battery then held its charge charge over night and did so for the first three nights however the battery failed to hold its charge the first time I kept it parked for more than a day. Any ideas? Suggestions?

Other info: AC compressor needs to be replaced. Brake light error code (brake light needs replacing) comes on sometimes but not every time I drive the car. Seller replaced the brake light right before I the purchase.