A car doesn't have to run to be able to donate the car to charity as some charities will fix the car if possible and sell it to someone to make their profit.
Others will sell the car off to someone who will then fix the car or use it for parts so the car doesn't have to be in running condition for the charity to accept it.
Just make sure you have the title to the car and let them know that it's not running and they will then let you know what you can write off on your taxes for the donated car.
I've donated a non running car to charity before and I was able to write off some on my income tax but not as much as I would have if it were running.
Still it was a nice tax write off either way and was much better than taking it to the scrap yard since the car was able to be fixed if someone wanted to fix it but I just wanted a different car.