986 S problem at idle, engine won't rev and shakes, battery disconnected

[tony_fury]

While not as experienced as the guy's providing you suggestions.
From reading all the different problems members have encountered on this forum, the number one item that resolves a lot of issues is the MAF.
While also noticing a very low battery will cause some very erratic behavior. If voltage levels are low, sensors can do some strange things.

Reading your post:
The problem started after you disconnected the battery to replaced the dash bulb. I can only assume that the battery was disconnected quite a long time while removing and reinstalling the dash.
My guess is the ECU is having to re-learn all the sensor readings all over again.
You also had the GPS installed for your insurance. (Was this installed after the bulb replacement) (Battery disconnect again?)
You state the GPS was installed on the positive side of your battery, is it drawing from the battery all the time.
(How old is your battery?)

Also reading you stated that after the Indy checked for codes, the car warmed up for half an hour and ran fine.
You have no codes.
I would stop with the 1 minute procedures. Let the car reach operating temperature and re-learn the air/ fuel mixture readings.
Possibly get a volt meter and check the battery voltage after it sits overnight.

My suggestion is to let the car run and warm up, let it re-learn.
Once warm, if it's running fine, take it for a a drive close by and don't baby it.

My 2 cents..
T