If your bike is still under warranty contact your dealer. Does you bike have any mods, such as different handlebars, extra electrical items? They are often a source of problems like these.

 

 

We have come to realise that changes to bikes that involve the electrics attract electrical problems like a magnet! Unfortunately there are many threads around HDF that have such mods at the heart of the problem. Those items don't raise any suspicions I must admit, but as your heated grips and starter can involve the handlebar wiring, I suggest you start by checking the right-hand one, to see if any of the wiring is damaged. It is a tight squeeze inside and easy to create a false ground by pinching a wire or two, when refitting. I suggest that as a first step.