1988 honda hurricane 1000F-will not start?

Probably burned out brushes on starter. Remove it and see. Sure, once you Get solenoid and  all to work again, the C/O ammeter will show what's what. But, it's Still fried brushes and commutator. 

  Possible mains fuse bad/open/bad connection, but all worked before. 

  The +  battery lead melted, like you said, this isn't in the mains circuit, it is direct path to sol. and starter.

   Check for bad connections at the primary cables, and  grounds. Remember, if the positive overloaded, the negative had same current flowing. Your  new problem might be in bad ground and/or connections to battery.

  Might have damaged the primary lead Connection To the mains fuse; it's often crimped into same lug. Most el. problems can be Seen , or Felt by pulling on wires/lugs. Overheated cable can melt the fuse or its internal connections, even though fuse never overloaded. I  grudgingly Admit, Exo  Might be right in This case. Eyeballing an ATO type fuse is 99% effective. The glass 3AGs  (not on your 'sickle) opened  Inside cap from age/vibration. 

 Get out the $6 Harbor Freight DVM. Read how to use DC volts and Ohms. 

   EDIT Your Battery Could be dead after that melee. Bench charge overnight. If it's  marginal, it only takes one such occurrence, or leaving ign.  on overnight, to ruin it.

I would use a clamp on amp meter to check the current draw of the starter motor.

If it is bad it will draw many times it's normal current which would explain a overheated wire that feeds power to it.

Blade-type fuses with little fusible wires often break right at the wire attachment to the blade, which is an almost invisible crack. As others have said, eyeballing fuses ain't good enough. ALSO, there may be a reason the solenoid failed. Might be time to pull the starter motor / solenoid assembly, take the starter apart and inspect the brushes, bearings, Bendix drive, and re-lube 'em. Also check the drive teeth. Didja know there's a spec on brush length? Why yes, there is. It's in the shop manual. 

Check the Main 30A fuse. 

Checking a fuse is not complete without checking if power is going to it and coming out of it.  Charge the battery.  Get a 12V incandescent test light, connect it to battery negative and check if there is power on both terminals of the fuses with key ON.

If there is power on both ends of fuses, check load power, trigger power and trigger ground at the solenoid while trying to start.  Good luck.

So now get your multimeter and continuity tester out and check the path from fuses to solenoid. Look for problems with the earth/ground.