I have one of these little 31cc Mitsubishi built engines on a bike sitting in my bicycle shop showroom. From my prior research, the motor internals were apparently interchangeable with some of Echo's backpack blowers!?!? The history of these units is as follows (by my same prior research): marketed by Kidde (the fire safety folks); orig designed for a fire dept grade smoke blower (hence, friction roller driving on rubber covered wheel of fan's drive spindle); then "re-thought" as a bike engine! This was purportedly due to Mac getting their smoke blowers to market first!
To all of those dealing with K&S "Bike Machine" issues, link for a free PDF download of owner's manual:
http://www.bikebug.net/manuals/Bike-Machine-Manual.pdf. It will cover all of the needed GENERAL stuff.
Relative to the issue of no spark, I tend to agree with everyone else on eradicating the surface-rust buildup from 30-plus years of humidity on new/unused metal parts. They may also have had a coating of cosmolene, or other protective lube, to negate same. In either case, getting to the spark system to sand &/or degrease is crucial. If you'd find a dead coil/stator/condenser/etc, you can source low-$ solid state conversions from Stens & other small engine pars suppliers; they've been out since before they built this unit! Make sure to source one for the 2-stroke, as 4-stroke units exist, too. I used one on a SKILL chainsaw which had the dumbest exhaust fumes routing method in history: cooling vanes on flywheel sucked the exhaust gas back into the points===D-U-H!?!?!?!? Ten bucks, plus an hour's work, solved it all.. Also had a vintage Puch dirt bike with a totally FUBARed ign system & did same to it.
If it ever DID have fuel in it you'll likely need to pull the carb off & do a full teardown. Salvage all gaskets by carefully removing from mating surfaces with a single edged razor blade. Plan to re-use: gaskets, rubber, plastic components, & float/needle/seat parts. If you don't have access to a heated, ultrasonic vibe-tank (3-stages using white vinegar; followed by a baking-soda rinse; followed by distilled water rinse), instead a thorough soaking/cleaning of the thing in laquer thinner (EXCEPT items I've listed above for re-use). HIGHLY FLAMMABLE!!!!!
BEFORE YOU TEARDOWN THESE UNITS: make sure that any nuts that retain shaft mounted items are NOT reverse (i.e.: left-hand) thread. It seems that the majority of the nut-N-bolt parts' descriptions in the manual are of SAE, & NOT metric, fittings.
As a life-long pro mechanic, AND bicycle shop owner, with a background in product design engineering, I want to broach the following: I have read some postings on other sites about these engines from people who advocate using glues/adhesives/caulks/liquid weld compounds/etc to repair these & other things. These are likely being advocated by the same ilk of folks who think you can buy a REAL bicycle from a store which also sells maxi-pads &/or Barbie-Dolls!?!?!? PLEASE REFRAIN FROM BOTH OF THESE PRACTICES; IT CAN KILL YOU &/or LOVED ONES!!!!!!!!!!!!!!!