Is it the alternator ? If when I jump start my car and it takes me down the road maybe a mile before it dies out and the whole time going I have no speedometor nor can get out of my car at all without getting it jumped started first

sometimes when your battery goes so does the alternator,did you notice if your lights started to dim,m check th battey sounds dead.

battery fauly

Sounds like a bad connection somewhere. Maybe the thieves or the repair shop damaged/loosened something. I would start the car and start wiggling/moving wires and connections to try to narrow down where the problem is. Start at the alternator connections, both at the alternator and where the thick wire connects, probably at the power distribution box but it may go straight to the battery; don't recall on that car.

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Maybe it wasn't running long enough to charge up the battery?
Stop trying to jump it, when you are having problems with it dying, take the battery off and have it charged. And/or buy a $20 voltmeter to see what the battery shows. If it says less than 12 volts, it is discharged, and needs charging. A good battery that is not run down should have at least 12.5 volts. A new battery that is charged should have very close to 13 volts, maybe 12.8 volts.
When you have the truck running, check the alternator for charging. You put the voltmeter right on the battery and check it again. This time, with truck running, battery should show at least 13.5 volts. That shows the alternator is working. A good alternator will put out about 13 or 14 volts-the regulator will keep it from going any higher to prevent problems, like a melting battery or electrical parts burning out.
I would say get the charging system working right, then address the problem of dying at stop lights. That could be a carburetor problem, if the alternator is working.

If the batt light is on, the alternator is not charging the battery.
If the battery won't hold a charge, it could be failing.
If you are having a specific problem with your PT Cruiser or Mustang, let us know what it is.

Could be a faulty connection with the battery cables, a bad ground, or any number of things. What do you have to do to get it started again ??

wow if your battery is that old i would get a different one but you can have the battery and alternator tested for free at a auto parts store they can tell you if its junk or not but thats why your having them problems when your alternater spins it charges the battery if the battery is no good it wont hold a charge and you car will die now it the alternater is bad it will not keep the battery charged and your car will die.

Taking the key out does nothing

I would have the fuel pressure and fuel pump
checked out

When it dies, it won't start back up? Does it crank over after it dies?

could be maf sensor