Turns on but turns off right after

they probably didn't set the valve lash correctly one of your cylinders isn't firing correctly get a cylinder compression tester and test each cylinder

You may have cooked the engine.
It sounds like the head gasket may have blown, and you could be leaking coolant into the cylinders.

Here are the cylinder head torque specs for Chrysler Town And Country 3.3l:
You will find a tightening sequence in the cylinder head bolt location-tighten the head bolts 1 to 8 accordingly using the four-step torque turn method
Here are the steps:
1. Bolts 1 - 8 to 61 N•m (45 ft-lb)
2. Bolts 1 - 8 to 88 N•m (65 ft-lb)
3. Bolts 1 - 8 (again) to 88 N•m (65 ft-lb)
4. Bolts 1 - 8 turn an additional 1/4 Turn, this step does not require you to use a torque wrench
Remember, after 1/4 turn, the bolt torque should be over 122 N•m (90 ft-lb). Otherwise, buy new bolts. Once all that is done, tighten head bolt number 9 Cylinder Head Bolts Location and use Tightening Sequence to 33 N•m (25 ft-lb)

You will cause the engine to go bad and have to replace if you keep driving,like a tooth ache,will get worst.

CHeck fuel pressure pump, if you need keep press to stay ON, it possible that some rpoblem in the injection system or fuel pressure or clogged injector/filter.

That happened to me once in about year 2 of owning it. 8 years later, it has not done it since. Glitch, who knows?

sounds to me like the throttle cable broke or is out of adjustment.

Make sure your testing cylinder 8. Ford numbers their cylinders differently that others. #8 is the rear cylinder on the driver's side of the engine. The ignition coil may be putting out a weak spark. It should produce a spark capable of jumping a half inch gap from the coil terminal to the end of the plug wire. Next step without diagnostic tools is to swap fuel injectors with a good cylinder. After that check compression and compare with a good cylinder (hold gas pedal to fully depressed position before turning key to "on" to place computer in "clear flood" mode so engine won't run when checking compression).

Could you please rate this solution, it was hard to find.

You have to get it (the lock cylinder) to turn otherwise you will have to replace the housing it is mounted in, if you get it to turn than put it in the run position with the key in on the right side there will be a small hole.put a piece of a coat hanger in the hole this will allow you to push up the tab to remove the cylinder,however if you are having trouble than the key will most likely worn excessively you will need the key to pull on to get the cylinder out if the Key will not stay in the cylinder then use a screwdriver to try to pry it out, if you are having trouble then here a two tips, turn the key slightly back I MEAN SLIGHTLY BACK and try again also if the vehicle has an automatic transmission remove the shift interlock cable from under the housing this will be a black plastic piece right underneath the cylinder,heres the key u will probably break the 3 little plastic clips no worries if and when u do this simply reattach it by wrapping a wire tie around it. PLEASE NOTE: This solution comes from a Saturn dealer technician and is correct.

if fuel pump stay running that one thing but it should not get the cylinder full of gas unless injector stay open if as soon you put the key on the injector open anf fill the cylinder that sound like our computer is shorted try another computer if its ok change the oil before you go the engine is full of gas hope it a fixya thanks pierre