Why does my car not start at times

The first thing to do is check the battery connections to see if they are clean and tight. If they are, go to a auto parts dealer and have your battery checked under load...they will do it for free. This will tell you if your battery is weak...which would explain why it is going dead from more pull being placed upon it by the heater fan. If the battery is good, and the connections are clean and tight, there may be a draw on the battery from a short or other bad connection that was initiated when the heater was fixed, so your best bet at that point would be to take it back to the dealer and have them check their work for an unintended draw on the battery. This could be the problem since your battery wouldn't start with a boost the last time, but bad cable connections could do the same thing and can be checked quickly.

Thx @DMS74.. I took it to the dealership. They said the throttle was stopped up. They had to recalibrate throttle and reprogram Ecm. And they did Engine De-Carbonization. Charged me 300 bucks.. Did I get screwed over.

Also when I drove it this morning, It wouldnt pick up speed, no more than 40mph.

You know your dealership much better than I do. I would have questions about some of what was done to your car being related to a problem with it not cranking. This is why its so important to have a dealership you can trust...if you don't trust the dealer you have its time to look for a new one. The best way to find a good dealership that can be trusted is by word of mouth...a good reputation travels quickly.