it might be your TPS sensor going bad, that is the sensor located on your throtle body. Just in case check your coolant level couse if it is low the car can do strange things like that too.
It realy sounds like a fuse. cause i had a similar problem a couple times. Check all of them again. If they are still fine then you might have a open wire some where.
it does sound like a ground problem. The charging system may work fine but there could be a loose wire in the system some where. That is a strange problem.