Have you checked the battery using a multi-metre? This would be your best bet to determine if the battery is in good health or not. It certainly sounds electrical as the "click, click, click" you hear is the fuel pump priming the carbs
You want to be seeing a strong 12V on the battery with the ignition off. Then turn on the ignition and see if / how much the voltage drops when you turn on lights etc. If you can get the bike started, test the battery again - it should be around 14V and this is to check that the charging system is working.
I assume you have checked your heated grip wiring, but just in case I'd suggest going over it with a multi-metre as well to make sure you haven't accidentally shorted something. How is it connected up? Direct to the battery, or via a relay?
Do you have any sort of alarm or immobiliser on your bike?