Okay, you have an electrical problem.
This is what I would do:
1. Have a close look at the fuse connections. The connections or fuses could be corroded, or the the fuses could be sitting slightly loose inside the connections.
2. Do a resistance test on the spark plug cable to see if the wire is not broken.
3. Make sure the spark plug Cap is properly connected to the cable, and make sure the other end of the cable is properly connected to the Coil.
4. Hook the Battery to a Battery Charger, and make sure the battery is fully charged.
You mentioned the battery is new - but that does not mean the battery is fully charged or the battery is not faulty. Hardly any battery that comes off a shelve is fully charged - you actually need to hook it to a charger to get it fully charged.
This is very important on our scooters with DC CDI's - the CDI's on our scooters need an almost fully charged battery to generate a proper spark at the Spark Plug. It is important to understand that on our scooters with DC CDI's the Battery itself actually generates the spark at the Spark Plug (Capacitors at the inside of the CDI as well as the Coil just boost power to give a powerful spark at the Spark Plug).
So the weaker the Voltage at the Battery - the weaker the spark at the spark plug will be.
Apart from charging the battery, the Stator on our scooters only triggers the CDI to release power to the Spark Plug.
If the battery is fully charged and the scooter still does not start, you can do the following:
1. Unplug the 2 pin plug at the CDI.
The two pin plug only has one wire - the thin wire on that plug actually feeds power from the Battery to the Spark Plug (via the Capacitors in the CDI, the coil, and spark plug Cable).
So while the two pin plug has been unplugged, you need to do a Voltage test at the single wire on the loose plug.
With Ignition Switch in "on" position and the Negative wire on the Multi meter linked to (-) on the Battery, you should get between 12 -13 Volt reading at the connection on the plug. (The same Voltage reading when you do a direct Voltage test on the Battery).
Then
With the two pin plug still unplugged, somebody need to press the Starter Button to swing the engine.
While the engine is swinging, you need to do a Voltage Test at the single wire on the loose plug.
You need to get a voltage reading of at least 9.65 Volts on the loose wire - otherwise you will get an improper spark at the Spark Plug, and therefore starting problems.
If the Battery was fully charged but the Voltage at the loose wire on the plug was lower than 9.6 Volts, it means you have a voltage drop in the power line elsewhere before the Plug, or the new battery might be faulty.
New batteries are not faulty that often - but in our country it happens fairly often.
You should get a proper load test done on the battery before you buy another battery.
If everything looks okay and the scooter still does not start - you could try a new Voltage Regulator.
I do not know how it actually works, but some time ago somebody on a forum elsewhere mentioned that a starting problem on his scooter was solved by replacing the Voltage Regulator.
Not so long ago somebody on this forum also could not solve a starting problem - I just can't remember his name or scooter model.
I mentioned the guy who solved his problem with a Voltage Regulator, the guy on this forum installed a new Voltage Regulator - and his problem was solved.
I hope this helps.