So, gonna jump right into this, my daughter recently bought a 2014 Honda Accord EX-L. This is her first vehicle purchase after graduating college/getting a real job, she's super stoked about it. She spent a lot of time researching vehicles, going for test drives, etc, finally settled on this particular vehicle. Long story short (as possible), when I drove it to the mechanic to have it check over prior to completing the purchase (mechanic gave it 2 big thumb's up), as I was driving it back to the dealership, I noticed the radio did not turn on right away when I started the car (noticed that the backup camera was not displaying as I was starting to back out of the parking spot by the mechanic). I tried the radio power button to no avail, looked around a bit to see if maybe I was missing something, then just started driving. About 4 or 5 minutes later, the radio turned on by itself while I was driving (as did the corresponding displays). I mentioned this when I dropped off the car, communicated the issue to the dealer, stated that that needed to be looked at, and that we needed to note that in the contract as a "we owe" if my daughter decided to go forward with the purchase. I then left for another engagement, the dealer spent 5 minutes trying to reproduce the issue, stated they could not reproduce, told my daughter I had likely just mistakenly pressed some button, and communicated to my daughter they were going to sell the car "as is" with no "we owe" in regards to the radio. She agreed top this, and we went to pick up the car a day or two later. While the salesman was showing her a few "lesser known" things about the functionalities in the vehicle, he started up the car, and the radio did not turn on. Three or four minutes later, it turned on, by itself (similar to the experience I had communicated to them). They were still resistant to trying to address the issue for her, stating that she should have spent a couple thousand more dollars for their special warranty. We did get them to try to diagnose the issue. They came back and told us that the battery was on it's last legs, that replacing the battery should resolve the issue. Daughter spent $180 on a new 500cca Interstate battery, she's still experiencing the issue... not every single time, but a good 40% of the time, and she says that the time to when the radio turns on by itself seems to be getting longer.

Any ideas on what could be the issue here? I'm uncertain how to proceed. Obviously this issue has somewhat chiseled away at the happiness my daughter was initially feeling with her very first car purchase.