Scooter without starting engine gets no spark?

I recently bought a scooter and it ran very well until recently.

It hasn't been doing anything recently and I've noticed that it's not getting any spark.

I probably wrecked the starter motor while troubleshooting because I took out the motor shaft and couldn't get the springs back in, but I didn't think anything of it because it only started with the kickstarter anyway.

I put in a new spark plug. I checked the wiring up to the starter coil and had a total of 6k ohms, which I thought was fine. So the coil was 3k ohms, and the connector was also around 3-4k ohms.

Does it even work without a starter motor?

My oil filter between the engine and the engine's exhaust valve is also completely dry. Shouldn't there be gasoline in there?

The only thing I can think of is that the CDI is broken. But otherwise, I'm out.

The carburetor is and can be very dirty, but before I spend unnecessary time on it, I want to get the thing running again.