Having resuscitated two old '86s, I'd agree with the others.
First, check your battery power. Use a multimeter. You need about 11.7 DCV to start the bike? 12.4 is optimal, but once you drop below the mid 11s, you might get enough power for your lights, but not enough to crank the bike.
I also use a no-maintenance battery and iridium plugs. I remember the difference was huge when I put them in, as far as ease of starting.
Second, check all your electrical connections.
If you have an assistant, (and if your battery is good) use a multimeter to make sure your starter is getting 12 volts when you press the button. If not, trace backwards from there. If it is, and the starter isn't turning over, it's a simple matter to take off the starter motor and clean it out. Use the on-line manual or a clymers.
One way or the other, I'd recommend taking apart all your electrical connections and tightening and cleaning them.
As far as gummed up electrical connections, I'd guess the most overlooked part on the bike is the ignition switch (the black hockey puck like thing under the headlight bucket). Remove the two screws, gently(!) pry off the cover, sand the contacts down, and you could get a noticeable improvement in electrical power and ease of starting. (The copper was green in there on one of my old bikes).
The second most overlooked thing is the starter button itself.
Cleaning these two things can make a difference. However, neither will help you if you don't have a good battery. It all starts with the battery.
Good luck and keep us posted. When you fix it let us know!
MF Battery, Iridium Plugs, RR relocated, Voltmeter, 170/80/15 Kenda Kruz rear tire, DIY Samsonite hard bags, DIY shaved seat with Beaded seat pad ('cause that's how I roll) and the dreaded STATOR CHANGE.
Shining Black Bess '86 VN750, retired for parts after a fried stator and being knocked (kee-runch) in her parking spot.