Here's the stuff I'd recommend you check if your moped only runs with the choke on (in order I'd try them):
For information on procedure refer to the message "How To Fix Your Moped".
1. Make sure you have fresh gas (less than two or three months old),
2. Make sure your exhaust isn't plugged up. Have you cleaned it?
3. Make sure that the carburetor is on the engine tightly and has a good seal.
4. Clean the carburetor. Make sure to clean the jets very well.
5. Make sure there isn't any rust in your tank (make sure you have a fuel filter while you're at it --if you don't just buy a cheap in-line filter (about $2) at an auto parts store and hook it up between the fuel tank and the engine).
6. If you have a decompression valve on the cylinder head (somewhere near the spark plug), make sure it isn't loose or dirty.
7. Check the timing. Use the cigarette paper technique to set it.
8. Make sure you have good compression. This is best checked with a compression gauge --borrow or buy one. You want to have at least 100psi compression (some of my peds are at the 160psi mark) --the higher the better. If you have crappy compression, watch the engine while it's running for leaks.
May the Force be with you.