I bought the bike used and it had a short in the left control and melted it. I bought a new one and the bike has no power in the run position but in the park position it has break lights.
Any ideas on what it could be?
It sounds like this is your ignition switch. If you are receiving power in the 'park' position on your ignition switch you are clearly getting power to some degree.
There is merit in checking all of your fuses as well.
You can validate various connections using a multimeter to see if you can detect voltage.
Here is a good post regarding multimeters.