Dayton, hmmm... That's not SUPER far from me. If only I had money, I could come fix your Tomos for ya, or at least tell you what the problem is. First thing's first, pull out the spark plug and make sure it's not all gunked up.
After replacing the plug, make sure you're getting gas. Take the fuel line off the carburetor and turn the fuel valve on for a second. Any gas? Is it clean? Is the tank dirty or rusty when you look inside the gap cap? If you've got gas there, you might need to take the carb apart and clean it. It's not as hard as it looks. I generally can tear one apart and clean it in about 10-15 minutes. Super easy, really.
Also, you might want to check the air filter. Is it clean? Is it even there? This is crucial.
Next, if it still won't run, you might need to take the spark plug out and check for some spark. Just take it out, re-attach the plug wire, rest it on the cylinder so the nut on the plug is touching metal, and crank it over once. Got spark?
Just remember, the three things you need for an engine to run are compression, fuel and a spark. Read Fred's moped repair guide. Lots of info. These are just some basic checks and some of the things you'll want to try first.
Oh, and that Garelli isn't that bad. I'd ride it if I had the money for it.