OK, no need for a voltmeter, you've already answered the question as to whether the wire is grounded or not. It is; and it isn't supposed to be.
Find out where the wire goes and disconnect it from whatever switch it is connected to. Reinstall the other end of the wire on the coil and see if the engine fires up. If not, the wire is shorted out. If it starts, the switch it's connected to is bad.
Replace whichever one of those two is defective.