2013 Ford Focus won't turn over

A week ago while on an errand my car wouldn't start when I returned to it. Dash panel lights/radio/seat belt chime all worked, however. Luckily the shopping center security had a jump box so after a couple of attempts the car started. Got it home, but then it would restart. Have a tester/charger, hooked it up, showed ok and fully charged. Still wouldn't start. Took battery out to shop to get another test to double check next day---battery was putting out 626 CCA when its rated 590 (a Motorcraft battery I'm sure came with car---I'm 2nd owner). Obviously tested good. Put battery back in car. IT STARTED. Drove on another errand and didn't switch off until returning home. After switching off would not restart. Tried disconnecting and reconnecting battery cables thinking it was a connection problem of some kind---several attempts over last few days. Has yet to start back, and now the car's electronic display is giving a "Low Battery" message, even after I left on the charger (slow charge, 2 amps) ALL DAY, with charger telling me battery is good and fully charged!! Any ideas? I know it has a starter relay that I've found and unplugged and plugged back in (but haven't replaced yet---$9 from Ford). This does not seem like an alternator problem to me but wonder if others had encountered anything similar. Besides that and relay, the only thing I can think of is starter is bad. (Also had someone recommend to me trying to start with the car in N---auto trans; also no dice). Obviously would welcome any suggestions/advice!!

I would guess you just need to do a good cleaning of the inside of the battery cables and the outside of the battery posts. Get them metal color clean. I know they have been unhooked and reconnected a few times, but they need to be clean.

If that doesn't fix it check the other battery cable connections. Kindly let us know what the problem was. Maybe you have it figured out by now.

Will be very surprised if dirt/corrosion is the problem. The cables/posts look brand new almost. (This model has a cover over the battery so it's been well-protected). I have not inspected the inside of the brackets that connect the cables to the posts but will next chance I have but again, there's zero corrosion, etc. on the posts or anywhere else that I've seen in my multiple disconnection/reconnections of the cables. Also getting some odd other things happening---after turning the ignition key 3 times in an attempt to start the car the trunk started popping itself open! Did this twice. It's also begun giving me 2 short horn beeps after hitting the remote lock on the key as if a door is open on it after I've confirmed they're completely shut. Starting to think this is some weird electrical/software problem. Probably towing to the shop/dealer tomorrow.