Over the winter I purchased 2, 2007 GTIs from a friend's parents who did all the proper maintenance over the years. I properly got them ready for summer, giving both brand new batteries amongst other things. During my 4th trip out, one of them died relatively early after launch. I noticed when it started, it sounded like it struggled, then eventually wouldn't start period. When I pushed the start button, I would get a single click, leading my Google searches to think it was a solenoid issue. I got them home and cleaned them out and attached battery cables to it and let it sit for a few minutes. I started it and it cranked (with the hose attached). I then detached the cables and attempted to start again but only gave me the single click. I'm guessing the battery was dead. This is a new battery which leads to me believe whatever system is used to keep the battery charged is faulty. Any suggestions where to start? Thank you!