New remote starter - worried I ground the starter

Take your car over to the local Advance or Auto Zone and they will hook up the scanner and extract the code that has activated the light. They don't charge for this service. Could be coincidence and more than likely is completely isolated from the starter incidents. Did you hear that horrible zipping sound when you hit the starts position with the key? Most late model cars have PCM controls that when the tach circuit sees a certain rpm level it disables the starter circuit. I know my Edge has this because I've done the same thing on it that you confessed here w/o any starter engagement!

I didn't hear any sound and nothing strange happened when I turned the key too far. I'll probably get the light checked out though. Thanks for the advice!

If the starter was engages you would have heard an unmistakeable god-awful whizzing sound. At least that parts is ok!