I have a 2003 pilot. My daughter was driving it and said the transmission started not wanting to shift so she limped it home. I went to start it and the battery was dead. Charged and checked battery it’s still good. Checked the alternator and it wasn’t charging battery. I put a new alternator on and the same thing it won’t charge battery. I though it was weird that the alternator, battery, and transmission all went out at the same time. With the battery fully charged it seems to drive and shift fine. When the battery drained she have no power or want to shift. I’m think problem between the alternator and battery. All grounds and connections seem fine. Also the battery light on the dash isn’t coming on. Any ideas?