Thanks everyone for sharing their experience and knowledge. Here is my experience after going through this magical situation for 4 days.

Case History: All of a sudden my Ram 1500, 2013 SLT starts getting on, without pressing any fob button. Vehicle was running, locked. No issues with operations of fob oriented opening and closing of doors, starting vehicle but after engiine is off, i am coming out- it starts again without key onside. Or / and when i start walking away - it starts on its own.

Forums- Youtube: Explored everything - and as a non technical guy- i came to know following treatment steps.

1. Check FOB - replace battery and reattach those small metal pointers inside fob buttons.
2. Check truck battery
3. Reconfigure Fob

Analysis: Fob was opened after watching youtube video - it was very ehelpful in understanding and i found FOB needed clean up , those golden points and also a small metallic button was loose - fixed that by gluing properly.
2. Came back to truck - now everything was normal- i mean no accidental starts but it was not starting with remote now. Rest all functions were normal.

3. Truck battery was checked - it was superb. Now I went for last step , option i had.

Reconfiguring FOB: You need metalic key - i inserted turned to right at RUN point- engine no start. Now, I pressed OPEN button for long press and then PANIC buttong without releasing OPEN button.

CONCLUSION: I started vehicle - and rhen shut it up. Chedked with remote - everything was back to normal. Remote starts working as good as new.