Car turns on with no Fob in it

Yesterday i drove my car from work to a local place to eat, it fired up came to life and drove fine. When i went to leave the place, i put my FOB in and got no response from the dash. I got a Jump and the main battery came on.

When i got back to work, i turned it off and at break (2 hrs later) i tried to turn it on again, and it gave weak dash lights and went off. Then it refused to come back on, so i closed the door and started to walk away and heard the radio come on. The dash was all lit up and no FOB was in the ignition. I put he FOB back in and turned it off again. I got a jump again and got it home, where i turned it off and back on gain with no problem.

Today I tried to start it it looked like a weak battery, so i turned it off and took the FOB out and sure enough about 30 seconds later the dash came to life. I put the FOB back in and the car cranked. I turned it off and took the FOB out.

What all of sudden causes this? Since i bought this used, I am guessing it has the original 12+ battery, it says Panasonic on that battery. When I do Diagnostics from touch screen, says 14.1V when running, 12.3V when in ACC mode.

Any ideas, i have a trickle charger and can see if that battery can be revived.

Car Info:
Prius Manufactured 11/03
No Navigation
No Mods
VIN= JTDKB20U140027523
Mileage=154,274

Sat 2 years in a garage before being sold to me in, had 57,284 miles when sold to me. Had 1 inverter pump replaced and dash recall performed.

 

Battery shows 12.4v steady, had a friend do a scan on the car. Seems the main battery is failing.

 

I have never been able to remove the fob if ihe car was on, I don't have the smart fob, just basic.