You have no better idea than I do that the valves aren't closing. Maybe they are...maybe they're not. I've had the bike less than 24 hours. ...
I've listed the reasons why it won't run: low compression and a possible ignition glitch. I never asked "why won't it run".
OK so you have had
this bike for 24 hours. What is your experience wrenching on
other bikes?
Yes, you have listed a couple of items that
might make it not run, includind low compression. You know what one of the primary causes of low compression is? Mis-adjusted valves. But...since that can't
possibly be the problem, go ahead and rebuild the engine. Don't forget to adjust the valves on the new rebuild.
Oh, and the ignition "problem"? As mentioned by KiwiGS, there is power at all times (when the key is on) to both coils. The points will interrupt the ground, causing the coil to fire. Apparently you have been lucky enough to have the engine stop with the same set of points open any time you have checked it. By connecting or disconnecting a plug, you are completing the circuit and yes, it will fire. There is no problem there, but you may as well replace the points and coil, along with the (probably unnecessary) rebuild.
Sorry if any of this sounds harsh, but we have offered suggestions and you blast them down, then admit you haven't even checked them, so we, as a group, will be moderately offended.
Since you don't know the history of the bike, does it not make sense to check everything? Compression check is a good thing to do. Valve check is supposed to be done every 3000 miles, according to the service manual. When do you suppose they were last done? Points should also be checked every 3000 miles. Again, when were they last done? Have you checked the battery condition and the ability of the bike to charge the battery? Sorry, I guess you can only do so much in 24 hours.
Don't forget that the carbs need cleaning, so you had better buy some new ones.
One other thing:
It's a 30 year old machine. I'm looking at rebuilding the top end because:
1...it may be necessary.
2...it can't hurt anything.
1...it probably is NOT necessary
2...the only thing it will hurt is your wallet.
Checking the valves will cost about $10-15 for a gasket, less than $10 for feeler gauges and about an hour of your time. If you need to change any shims, they are less than $5 at Z1 Enterprises.
Rebuilding the top end will cost several hundred dollars for the parts, about $100 for a gasket kit and you will still need feeler gauges, and it will take considerably longer than an hour.
Why not just check the easy stuff and do the harder stuff if, and when, it becomes necessary?
.