Sounds like the Equinox (not just yours) is turning out to be quite a problem child. Try checking relays, maybe one or more of them burned out.
After you fix the problem, you may want to consider getting rid of that thing and finding something more reliable. I would avoid most domestic cars from right before the big bailout. The whole reason the big 3 needed that bailout was because of the poor build quality of so many of the cars they were making at the time and all the repairs that had to be done under warranty as well as people recognizing the problem and staying away from domestic cars. I'm guessing the warranty is long since expired and I promise you there will be more problems to come. Other electrical problems as well as transmission problems seem to be pretty common with the Equinox. More headaches, a hole being eaten in your wallet, and you as the owner doing a lot of this:
