Does it when vehicle not running either... The battery and its connections are good. I'm dreading a moduleMaybe the battery is just strong enough to start the car but not strong enough to power much else when it's running. Does this only happen when it's started or also when it's off and ignition turned to on? Get a voltmeter and check the battery voltage. It should be around 12.6v sitting there. If it's more than 5 years old maybe just replace it. The date code will be on the top or side of the battery.
When the car is running check the voltage on the back of the alternator charging post under the rubber cover. Make sure that you put the voltmeter or multimeter on a good ground and see what the charging voltage is. It should be about 13.5-14.5v.
Also, check your battery cable posts and cable clamps for cleanliness, tightness, and no corrosion. Check all your ground connections to make sure they're tight and corrosion free. Sometimes a little factory paint between the ground and the strap/cable/wire prevents a good connection.