98 Jetta...stopped while driving

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

is this the model with the elec water pump?

Have you had your alternator checked ?
If there is no charging from the alternator the "problem" will be solved as long as the new battery retaing its voltage. As soon as you start to use power you drain the battery. it's a bit like putting air into a punchured tyre ..... its still punchured . Could be your original problem ! ! Good luck

hi
have the alternator checked ( the rectify may gone down causing the said problems )

It sounds like your alternator might be starting to go bad and the Battery Light is coming on because it is not charging the battery correctly. Have your Alternator checked with a volt meter, it should be reading 13 to 14 volts if working correctly. If not, replace your alternator.

Try replacing your Engine Coolant Temp Sensor, it's cheap and easy to replace. Just remember do it when the coolant is cool to work with before you start cracking a pressurized system.

needs a new alternator, going down the hill, your RPM's dropped and all of the draw on from the electrical system came from the battery, and caused the battery to die too

It sounds like the alternator belt or the alternator is going bad. The squealing sound was probably the alternator belt. the alternator belt might need to get tightened or replaced or you may need a new alternator. The alternator keeps the battery charged. When the alternator goes bad the battery can not be recharged. You also should keep the power steering fluid up to par or the power steering will go bad on you.

Alternator is bad. It is not charging the battery as you drive.

try making sure all belts are tight jode