First off, try a NEW plug. Even if it looks good, it can still be duff.
Second, check the coil. Is there a purple band around the HT wire near the coil end? If there is, it's a 'ground to go' coil. There aren't many of these around, but there are a few. If that's not it, you have a duff coil. This is NOT a common fault on this particular engine, BUT the last TC200 was built a good few years ago, so I suppose it's possible that moisture has seeped in and shorted it.
The engine needs about 400 RPM to produce a decent spark - officially. In practice, it doesn't need a lot - a half- hearted pull of the string will easily do it. I've accidentally started a Flymo fitted with a TC300 whilst changing the blade - simply by rotating the crank with an impact driver (130 RPM on a good day!).
phil_saunders(a)bigfoot.com
Phil Saunders
May 2011