2007 Dodge Nitro: dash HOOD ajar light wouldn't turn off.

more then likely it's a door ajar switch - not a sensor .
Anti-Theft- Perimeter Alarm System
The perimeter anti-theft system provides for vehicle security through an audible and visual notification if the vehicle's exterior is invaded without the system being shut off. The system self-arms when the doors, liftgate and hood are closed and the key is OFF. Any open door, hood or liftgate will prevent the system from arming. The hood ajar switch, door ajar switches and liftgate ajar switch cause these circuits to register as normally closed circuits. The vehicle security module monitors the status of the hood ajar, door ajar and liftgate ajar switches. If these circuits indicate an open entry point, the switch opens the circuit to the vehicle security module, which energizes the horn and autolamp relays (causing the horn to sound and the lights to flash). The vehicle security module turns off the anti-theft system when it receives a command through the keyless entry keypad, remote keyless entry (RKE) transmitter, or anti-theft alarm inhibit switch.
https://www.youtube.com/watch?v=egIGBzO065U

Open the front doors and look on the sides of the dash for a pop off panel

Either a bad switch or bad ground. Find switch and see if you have power there.

no you get from under the hood passenger side

On the drivers side lower panel left side or in the center. If your looking for the release on the hood its usually a tab under the grill or a tab will pop out from the grill area.

Your owners manual should tell you, but look under drivers side dash as well, for a black panel that you undo , and drop down to expose another fuse panel.

The diagram is usually under the hood on the radiator support or underside of hood. If not autozone will give you free diagram.

This link should help you. Also you vehicle came from the factory with a diagram under the hood somewhere.
http://www.aa1car.com/library/serpentine_belt.htm

asd/ignition relay shorting or possble pcm/gem failure. Depending on mileage, I would return to dealer as this is a warranty issue.

In the fuse box, under the hood on the drivers side. There is a detailed map of what fuses do what on the inside of the box cover.