[wiredgeorge]

A burnt coil will not affect the battery discharging.

The battery on STREETBIKESONLY's bike is discharging. While operating the bike, it is operating from the power of the battery ONLY. Three things can be wrong:
1. bad connection (wiring issue)
2. bad stator/generator
3. bad regulator/rectifier

To fix the bike, first start with the easy things. First, recheck the battery connections. Make sure the connection to ground is tight on both ends and make sure the RED wire is securely connected at both ends. Make sure you didn't accidentely disconnect the white/red wire that also connects to the lug on the starter solenoid that the end of the red cables connects to.

Under the large forward cover on your bike is the stator/generator (not sure which it is but principal is the same). Out of this cover comes a number of wires which will include three wires that connect to the regulator/rectifier in some fashion. The connection can be directly or via a junction panel. I am not familiar with the wiring on a 636. In any case, disconnect the connector and clean/lube it. If you disconnect the connector, and have a multimeter, you can check the stator/generator by starting the bike (will start fine if the battery is charged). Look at the open connector on the stator/generator side. Note that there will likely be THREE wires coming from the stator/generator and they may be yellow. Anyway find the three wires, regardless of color and start the bike. Put the probes from your meter on the contacts in the connector that are connected to the wires coming from your stator/generator. At idle, I would expect about 50 Volts AC ANY way you put your probes. Check all the different permutations... in other words across all pairs of the three connectors. If you get LESS than 50 VAC, then the stator/generator is likely BAD! Get a manual for your bike and it will tell you the actual expected AC value and other checks to determine which stator/generator component is actually bad. If the stator/generator turns out be OK and it likely will, then check the regulator/rectifier.

Reconnect the stator/generator to reg/rec connector. With the bike at idle, put your multimeter into Volts DC (VDC) scale. Put the probes on the battery terminals. At idle, you should see nominally ~12.5 VDC. If the value is HIGHER, then the regulator/rectifier is BAD for sure and if it is lower, the reg/rec is either bad or there is a bad connection... check the connections before writing off the reg/rec. If the reg/rec is OK at idle, then go to the next step....

OK... the bike is still idling, twist the throttle so that the engine speed goes up to 4K rpm. Check the voltage at the battery terminals the same way as you just checked it at idle. At 4K rpm, it should read about ~14.5 VDC. If it is HIGHER, then the reg/rec is definitely bad but if it is lower, the reg/rec MAY be bad but again, there may be a bad connection. Since you have already checked the stator or generator (whatever it is called on your bike), this isn't the cause of your woes.

One of these checks WILL find the problem. While checking the stator/generator and reg/rec seem to be the most technically complex, a bad connection is usually the culprit and is usually the most difficult to find. Check all connections for the reg/rec. Have a can of contact cleaner (computer stores or Walmart) and some dielectic grease on hand and clean all those connections and put a dab of dielectic grease on them. Make sure the battery cables are snug on both ends. Make sure the white/red wire from the regulator/rectifier to the lug on the starter solenoid didn't get disconnected.