Q: It won't turn over, I even gave it a boost - no luck!

Van started 3-4 weeks ago even though battery seemed low. Yesterday tried to start it - did not crank over. Charged it for 2 days, first over night at a Trickle charge of 2Amps then next night at 24 Amps. Went to try starting it, not even a single click from the starter/seloniod. All interior and exterior lights work. Head lights do not dim when attempting to start engine. After that, I tried recycling the key quickly, as asked by a mechanic, no luck. Then not only would the engine not crank over, but I noticed that the R (for Reverse) was lit up on the gear selector, and I couldn't get the key out of the ignition. I continued to try to get the shift lever out of Reverse, but the shift lever felt like it was still in Park, then key suddenly pulled out of the ignition. After that the key has continued to work without issues, but still no crank over. Is there a possibility of a "lockout" switch or program causing this, or maybe stuck in Reverse ? Thanks for your help, John McLarnon

My car has 278086 miles.
My car has an automatic transmission.