Weak battery. You might measure 12 plus volts with the engine off but measure the voltage delivered when the engine is cranked. It will drop even with a good battery but with a failing battery the voltage drop will be very significant. I can't remember voltages but as a guide above 10v when starter is turning is good. The low voltage does all sorts of weird things to your dash like needles bouncing etc. If you hear a clicking this is because the solenoid doesn't have enough current in its electromagnet to pull the starter motor onto the engine fly wheel and it keeps disengaging. A new battery might not solve this as it is possible that the fault is with your alternator. Check the alternator is delivering charge when the car is running. If your still getting a dead battery then maybe something is drawing current when the car is off.
An aa guy will see this all the time. Call them out if you're a member they will diagnose very quickly.