I just bought a new car and three weeks later it has an electrical problem, can I get the dealer to give me a new car?

No. The dealer will fix it under warranty.

The dealer is allowed to fix it, if the issue can not be fixed ( they can replace an entire system if they needed to)
But you have to allow them at least a couple tries to fix the problem.

AFter that, you review your states lemon laws, but all of them allow the dealer chances to fix it first.

New: [noo, nyoo]
acronym, abbreviation

NEW stands for Never Ever Worked.
:)
Sad but true, Father.
The dealer has to be given reasonable opportunity to repair your car. :cool:
You have some responsibility in this, too. You must allow them to test and diagnose your vehicle, which means that you'll be without it during that period. :mad:
That is one of the disadvantages of a NEW car: nothing on the car was test driven before you got it. YOU are the test pilot but your also covered by their warranty.
That means though you'll be without your new ride, you won't be charged for them to fix it. :D