I have a 98 chevy prism. when i turn the lights on the car shuts down. when i turn on the defrost on it jumps like it wants to cut off. We took the whole dash loose and dont see and burnt wires or anything. What could it be?

is there any check engine lights on? also a leak in the vacuum lines will make it jump in and out of over drive. could be a few problems. wish i could help more, sorry. if you have a vacuum leak it would also make you heater controls not work like they should, like if you put it on defrost it will only come out the vents and so on.

you mentioned new alternator and battery, but it seem that the alternator is not charging, when you install the new battery the car started and run and after hours of running specially if head light is on the car shuts down. this is an indication that the alternator is not charging. (factory defect) have it checked or return part to auto supply.
if alternator is good and you have the car jumped and run it will not shut down even if your battery is dead because the charge of the alternator is enough to power the electrical system of the car until you turn it off. this applies to all cars

It's possible but unlikely. Still sounds like your battery is shot, and if so, jumping it may not work. First I would take it out and get it tested. If OK, your next step would be to check error codes (DTCs) with a code reader to see what's going on.

take a truck diagnostic tool to check, the NEXIQ 125032 plus software can do.

have the alternator checked. if the alternator is not charging the vehicle is only supplied with what power is stored in the battery. once the battery is dead there is nothing to charge it

your check engine light will give you information that will help solve the problem-get the computer scanned, go to a retail auto parts store, they all do it for nothing. Write down the actual codes, and come back here with the codes, you will get the help you need.

Sounds like the battery dies, or the alternator has stopped charging and the battery lasted as long as it could. Battery water, voltage while off and then while running if you can jump it.If you think the battery is good, take the alternator off and take it to the parts store and test it, if it is neither of those 2 , then the computer died. Check it out.

We had a similar situation. It took the dealer a few days to figure out it was an issue with the wiring harness(es) in the center console - around or behind the transmission shifter.

Try changing the distributor cap, rotor, plugs and wires

it's a default sensor to keep from blowing motor, you need to check your radiator for leaks. If that doesn't fix the problem , change your alternator. :)