So the engine spins freely when you remove the spark plug, but the engine doesnt spin when you have the plug in causing it to have compression?
So garelli used these weird rubber clutches. They work, but are dumb. This is where I would begin with any new to me garelli, vip or noi....
Step 1: purchase 30w NON DETERGENT motor oil. Most auto parts stores should have some, or I have heard that home depot has "compressor oil" that is the same type of non detergent oil.
Step 2 : change the transmission oil. Try to drain the oil into a clean pan to see if there is any metal flakes coming out. There should be a little shimmer, but not chunks of metal... gears wear down. Filling the oil is tough. That tiny hole on the side is not easy. I use a very large syringe with some fuel hose attached that fits into the oil fill hole. I just fill until it starts coming out of the hole. You can find the exact specific amount via the wiki here, but if you let it drain off the fill hole it will have the right amount.
Step 3: all mopeds of a certain age... change your break cables and tires and tubes. It's just your life my guy.
Step D: clean the carb. I mean really clean the carb. I feel like I should say to clean the carb. Get brake parts cleaner rather than carb cleaner for this. I like a nice tooth brush and I get a thin sturdy wire to poke thru the tiny jet holes. A strand of brake cable works well, or the twist tie off your loaf of bread, without the plastic coating. And fill your tank with fresh pre-mix. Everyone has their preference on oil and mix ratio. I just get oil that isnt the cheapest and doesnt show a chainsaw on it... I mix 40:1... no good reason why, i just like the extra lube but 32:1 seems excessive unless you are over 10k rpm
Step 5: new plug. Reference a ngk b6hs they should have these or equivalent brand at the auto parts store. Get a good one, actually buy the 4 pack.
Step 6: start up your new bike, ride around and feel life in your heart once more.
Step 7: #&@*%%$#!!! And come back to ask us a more specific question on how to fix a new problem. Got dang mopads!
Step 8: have fun, it is a great hobby.