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Check vacuum lines and make sure no holes, cracks or they are not connected. You can use a carb. cleaner spray on them and listen for a change in rpm's when you hit a bad line. PCV elbow hose is a usual culprit.
Put a gallon of gas in. If it starts, your fuel level sender has failed and you are actually out of gas. If not, refer to answer #1. May need to turn key a few times to prime the line.
Is it engaging properly? If so, may just be the bulb is burnt out. Otherwise, refer to answer#1.
Agree with #1. If that doesn't work, if automatic, shake the shifter back and forth and back to park or neutral and see if it starts. If it does, it may be the neutral position safety switch located under the shifter cable on the trans.
If this vehicle has a vacuum harness to the vent control system, follow the line through the firewall to the vacuum pump and make sure there are no breaks in the line. You will know from past experience if it was a vacuum setup by when you adjusted the direction you probably heard an 'air slurp' as you switched from floor to defrost etc.
Read this for the procedure. Just remember that the alternator removal, once unbolted, is like playing tetris. Only one way to wiggle and fit that part through and out and back in: http://www.fixya.com/cars/t2306920-trying_remove_alternator_from_car
Agree with prof. "The gear shift feels like it isn't connected to anything." Then it probably isn't. Follow the shifter cable to the trans. arm and see if it is still attached and tight. Otherwise, something broke at the other end inside the car.
Agree with#1 possible exhaust restriction. Also, have the cat. converter checked, that is probably what you are smelling.
Sounds like a break in fuel line. Need to have inspected ASAP.
You can try disconnecting the battery and waiting about 10 to 15 minutes and reconnect the battery. This should clear the light and reset the computer.