When dealing with a 2-stroke motor there are a few things to check first:
1.spark
2. fuel
3. compression
You have spark.
It doesn't sound like compression is an issue, and i don't think you had a soft seize. You can get a cheap compression tester at harbor freight.
Fuel: you've got to clean the carb. I suggest spending the $25 to get a can of carb dip. You can use it over and over again and if you continue to spend time with a two stroke - you will need it. Guitar strings are a good tool to help clean out all the little holes and some spray carb cleaner can help get rid of specks of crud that are sticking to the carb.
here is a good guide to cleaning the carb:
http://hondaspree.net/phpBB3/viewtopic.php?f=5&t=5389 Often times the simplest explanation is the right one. I've never had a CDI go out on me, but i'm not sure that is the issue.
Good luck.