One would have to assume that you're talking about a kill switch wire. How do you shut the engine off with the wire disconnected?
Use a voltmeter to check to see if the wire you're talking about is grounded. If so, it must have a short to the frame somewhere or the switch is bad.
Thank you for your help! Was thinking bad coil wire. Switch cranks mower fine with coil wire disconnected. Just trying to find out if anything other than the switch or bad coil wire would cause this problem. Can shut off the engine by touching the wire to the bracket that I disconnected it from!
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.