shaking, chattering, slipping noise and feel from transmission?

I have a 2008 Prius Touring model and experienced the above symptoms after having not driven the car for about 6 weeks. It started acting up after I backed out of the garage and while in reverse and my foot on the brake pedal. It shook quite a bit for about 15 seconds and then stopped and seemed to drive normally. I drove about 3/4 of a mile and entered a parking lot to park and while in drive it started shaking and making noise for a few seconds and then it quit and ran normally and has since then. I also had a hard time trying to get the remote to activate the door locks but eventually suceeded. The one other odd thing that happened was that the morning after the above incident, I went to start the car and a light on the dash came on showing an outline of a key and the car wouldn't start. I then used another remote and the car started fine. I realized the battery in the one remote was dead and have changed it. What I was wondering was whether the failing remote battery was the cause of the shaking, chattering,slipping noise from the transmission? I'm due for a transmission fluid change and will do it soon.

 

Thanks for the reply. It makes sense and I'll have check the battery which is old.