After not riding for nearly almost 30 years, about 2 years ago, I picked up a 1996 LS650 with 22k miles on the speedometer. I live in the Cincinnati are and thought I would use it for a little commuting and weekend leisure riding.  I’m certainly glad I found you all.  I’m not a mechanic, but I’m not afraid to try fixing things myself if I have the tools and there isn’t a great risk of ruining something or making it unsafe. I haven’t done any modifications, just replaced a lot of missing parts, fixed oil leaks, got a paint job, new tires, new fork seals.  It runs very well.  But I now have electrical problems I haven’t figured out yet and electrical systems and testing is beyond what I currently know.  Although I have read much in this forum and site, this is my first post.  

I first started having intermittent problems with the ignition switch.  I would turn on to the first position and 2nd positions and no power appeared to electrical items.  After I waited a while or switched it on and off several times, it would work.

About the same time, another issue appeared. When I would turn the key to the first position, I would have taillight, turn signals and the neutral light, but not the headlight or horn.  Oddly enough, both amber turn signal indicators would also dimly light.

I replaced the ignition switch, and that problem went away.  I still had the problem with the headlights and horn.  I removed the headlight and found a connector brown and melted.  I replaced it and no more problems, all went back to normal,  for a few short runs.   After a few hours of running, the headlight dimmed to a very slight glow and the horn stopped working. All other signals and lights worked as they should, but both amber signal indicator lit up again.  Other than that the bike started and ran fine.

I rode it in this condition for maybe an hour or 2 then other day, after I put down the kick-stand, the engine was killed as it should, but now in addition to the headlight and horn, it won’t start. The fuses I believe are good.  The battery is new and fully charged but it seems as if the starter isn’t getting enough juice. I'm think all these issues might be related.

Any ideas where I should  start at this point?  

Me too! the battery ground runs from the Neg. post , to a casing bolt on the right side above and in about 2 " in from the oil level window .
   You might also want to recheck you're wiring ,I think the headlight ,running lights , horn ,turn signals , all share a common ground wire .

Get yourself a tube of dielectric grease, and every connection that you take apart to inspect, grease it.  If you "believe" your fuses are all good and don't have a meter to test them, for the price of a few fuses maybe replace them with new for good measure and just tape the old ones to the wire harness as a back-up.