Posting this for my dad since as a older mechanic he is out of ideas and as the semi-techie son who watches a lot of Scotty videos I'm out of fresh ideas.

Here's the context. My father has purchased a used 2007 F150 5L automatic transmission (pretty sure just 2WD).

Since he's gotten it, he has had "weird" issues. Normally the weird issues manifest themselves as when turning the key absolutely nothing happens (no cranking, nothing) or the car will crank and crank and crank, but never turns over. When this happens they are not able to jump the car and it must be towed.

Each time this has happened my dad has fiddled with the battery cables. (Normally by taking the battery off to charge or replace the battery entirely.) Most often after he disconnects the battery he'll test it and the batteries normally show fine or maybe weak, but not in the needs replaced category. (Yes this has happened on multiple batteries, I think he's up to battery number 3 now.) He'll drop the battery on a trickle charger for 15 minutes or so and then try again and voila! Problem solved...until a month or so down the road and it isn't solved.

Keep in mind this truck has yet to throw a code.

This last one threw me for a loop and may be a completely different issue. The truck started, but would not leave park. When he turned the key off and removed the key the truck stayed running. (Freaked him out for sure.) The truck only shut off when he let his foot off the brake pedal. (He states that his hazard lights were solid on.) I'm not gonna lie in his Rav4 he's been known to hit both the gas AND the brake pedal so...he might have accidentally triggered a safety feature that if the gas pedal is on the floor we're not changing gears afterwards his truck started just fine.

Since I looked for codes with my equivalent to a BlueDriver (nothing fancy, but handy in a pinch) he has ruled out the computer and believes if he takes it to the shop they'll know right what to go to in 10 minutes or less. 

I'm thinking that this truck has electrical problems which will take a good amount of time for a decent mechanic to track down and then there's the cost of fixing at a minimum the first problem they locate and there could be multiple problems to locate.

Odd thing on this truck one of the battery terminals has 3 cables coming off of it. (I forget if it's positive or negative. Throwing that out there and wondering if that was standard or maybe evidence that someone has fiddled with the truck's electrical system already.)

Any thoughts/suggestions? Experiences with that particular year/model that might explain such behavior. Mileage is around 160K.

Thanks in advance.