That's the condensor.
The two coils on back plate are :-
left, source coil for ignition,
right, lighting coil.
You have a half wave rectifier somewhere as battery is required for indicators and tail/brake light (headlight runs 'direct' AC)
If wire is off condensor it won't spark
Probably no connection between source coil, points, condensor and ignition coil
I would check price of new points and condensor.
If Yamaha dealer isnt interested, try Suzuki TS100/125, GP 100/125.
Aftermarket is also OK (maybe eBay or in Britain?)
Your going to have to buy or borrow a flywheel puller (less than $10.00 aftermarket) and a 17mm socket. (remember lefty loosy
)
(it's possible to remove flywheel without one, but generally destroys it)
The woodruff key should stay in 'slot' in mainshaft but check.
The points gap also adjusts timing so is pretty important.
You can check points cam when you have flywheel off, its about 20 thou higher than rest of boss that fits onto crank.
If you don't have a multi-meter, get one, doesn't need to be expensive, $4.99 Harbor Freight special does everything you need
Rocan,
Don't know where you got CB100 from?
DT100 is a two-stroke, it's pretty easy to modify for more performanceif you know what your doing. (which I do ;D)
Even stock as a trail bike (wide bars, upright riding position) it will easily do 65mph
Modified plus clip-on+rearsets, somewhere around 90mph+