My 2004 Ford Taurus shakes when I start it and then cuts off unless I keep my foot on the gas. When it cuts off the battery, check engine and oil light comes on. It'll start right back up, but again it will not stay on unless I keep my foot on the gas. What could this be? I just had it fixed for idling issues, a blown fuse and brown coil (I think).

If you have recently replaced the battery, disconnected the battery or had to jump start the Taurus, you have likely reset the electronics.

The result of this reset is that the engine control module needs to relearn the running parameters including the idle point.

It take several minutes of idle/driving to reset the baseline parameters and during this interval keeping the engine from stalling is a challenge.

Hope this helps?

Engine Stalling After New Battery Fix It Like Pro

Could be Head Gasket blown , has no effect on oil level but will give you the warnings that have come up

You haven't given enough info to diagnose the problem. Did the car die while idling? Could it be restarted? Will it run if you keep your foot on the gas pedal? Etc...

sounds like fuel injectors

Throttle body bore and plates may be carbon coated . TPS may be getting old and have dead spots at and near idle position .

Could be a faulty idle air control valve, or dirty throttle body.
The computer controls idle speed by the amount of air passing thru the valve.

sounds like your idel motor/solenoid

try a fuel filter or have the injectors cleaned

keep your foot on the gas until the car warms up

have you tryed replacinge the battery