Yeah I can vouch for this, my chappy is good for 35/40 on the flat if I make myself small.
JT sprockets used to provide a list on their website of sprockets, usually plus or minus 2 teeth each side.
So, for more top speed you could go a tooth larger on the front and one smaller on the back, or keep the front the same and go two smaller on the back, chop and change until you find one you're happy with.
Bear in mind though, even as an 80cc the chappy was never really designed to go fast at all, it's only a 2-speed auto. (4 speed manual rarely), how fast do you really want to go on a small tube frame with laughably small drum brakes and iddy biddy tyres?.
As for the non starter, why not? Got spark? Fuel? Ignition?.
Take the side cover off, clean and gap your points and spin it up on a drill, it might just need a bit of encouragement to get things moving if it's been stood a while.