Hey dlh, welcome to the forum. You should find all kinds of help here. First off, not that it matters much, but do you have an '86 Kawasaki KLR 650, or a KLR 600? I believe the 650's came out in '87. Not that it matters that much. The bikes are quite similar, and I imagine that what ever is causing your grief will apply to either bike.
For some reason, my suspicions lean towards that new battery you have. If possible, take it back and have it tested. If you have a voltmeter, a 12-volt battery that is adequately charged will display a reading between 12.5 and 12.8 volts. The sealed AGM and Gel-Cell battery voltage, fully charged, will be slightly higher in the 12.8 to 12.9 ranges.
That KACR has been the culprit of starting issues. I like to start with the simple things and work into the more complicated [meaning expensive] diagnostics. If you can rule out the battery and / or starter as being the source of your woes, we'll help you through a plan of trouble shooting. Any other information you can give us about the bike, its condition, etc. will be helpful.
Again, welcome to the forum!
“many a trip continues long after movement in time and space have ceased”- Steinbeck, [I]"Travels with Charlie"
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