If the car is driving down the road or stopped but revved to basically any rpm above idle,
and you then use any voltage IE switching on a/c or high beams,
the radio turns on and off once and/or car lurches once.

I jump started a car yesterday, for what its worth.

I'll test the battery later today, but if its fine, point me in the right direction.

 

Check for secure connections to the battery, also the connections on the big ground wire from battery minus to the frame and transmission.

 

You also might want to check whether the alternator belt is loose or slipping.