HI. The idle thing is normal on those Grands. If the PCM loses voltage it forgets it's correct idle air control setting and has to re learn where to set the idle air stepper motor in order to achieve the correct idle speed. The thing to do is start the engine using a little throttle, then gradually back off the gas until the engine rpm drops below idle and the engine management takes over. It will usually take several attempts before it gets it right. If you have had a flat battery, charge it for 12 hours with a proper charger rather than just jump starting and relying on the car to do the work. Even with a fully charged battery a Grand can kill the thing if left standing for more than 60 days. If it still goes flat after a couple of days once you're sure the battery is 100% ok you need to start looking for an excessive current drain somewhere.