What I'm getting out of this is. The engine would turn over just fine but wouldn't start until you released the start button at the right moment.
If true? I see where the starter is drawing a lot of current and taking away from the CDI. Now that the CDI was replaced, it works fine.
This tells me the CDI either had a bad (or going bad) component and wasn't getting the current it needed to complete the circuit until the start button was released. Only then did the CDI get the current needed to fire.
My personal choice would have been to check and test the battery. I've seen where a battery would turn the engine over, but didn't have enough left to fire the engine electronically. No sparkie....No runnie.
I could be off base here (wouldn't be the first time) But this is my take on things.
By the way....If you develop the same problem in the near future? Check the battery, the connections, and the frame ground. These have caused more problems than I care to remember.
Oh, and thanks for letting us know the problem and what you did to get her going again. It's always nice to put this info into the memory bank for later use.