There is a huge difference between a VIN number and a serial number .
The point that a few people kind of bypass is the fact that the limiting speed (at least in Florida) is 20 mph for a bicycle and 30 mph for a moped.
Anyone with a gas powered bicycle, knows that 20 mph is easily bypassed by just about any china girl.
That would preclude it as a bicycle, since 20 is the max.
So the only other alternative is a home made moped.
Now the problem arises that there are no VINs for bicycle frames, so people will make them up. (You are aware that a VIN is the determining factor for DOT approval). And yes, I know that there are a few bicycles out there, that you can achieve speeds higher than 20/30, BUT they are SPECIFICALLY made to do so, and on NONE of those, would the manufacturer say, "Yeah, throw a motor on it" as it would then not be the same functionality, as the structural integrity would be compromised and it wouldn't be structurally sound with the added weight/torque.
How many of you with the "homemade mopeds" have, DOT approved frames, DOT approved tires, DOT approved lights, fully working directionals, stop/brake lights, etc?
(Everything that is required for a moped to have/be in order to be used as such on the roadway..)
Also, mind you, you're not allowed in bicycle lanes (or sidewalk) with the motor running, which was ultimately the OP's initial problem and what eventually lead to him needing a license.