Bear with me, I'm not much of a mechanical person (I'm better with computers than with vehicles, haha). So try to keep that in mind when you reply.
Backstory: I purchased a Kymco People 50 in 2007, brand new. I was in a minor accident with it a few days after I began riding it (inexperience can really get you!), and subsequently didn't do anything with it for about two years, during which time it was being stored in a friend's garage. In 2009, I decided it was about time I started driving it again, so my friend took it to the shop to get everything up to speed (new battery/spark plug/etc). Supposedly, said friend drove it back to their house (meaning the trip to the shop was successful), where it sat for about a week until they could deliver it to me (in a van). We unloaded it, I parked it behind my house, where it sat for a while (it was winter, didn't want to drive it in the cold). I started it up once during this time, and it ran fine (but I didn't actually take it anywhere; just around the yard). I attempted to start it several OTHER times throughout the winter, but other than the one time, it wouldn't start. It's like it just decided not to work one day.
Kickstart produces absolutely no results, and when I try to use the electrical start it'll turn over, but doesn't "catch". Headlight only works when I turn it on high, horn and blinkers work fine. Clock does not work (but that runs on a separate battery, right?).
What I've tried:
Recharging the battery
Changing the spark plug
Refreshing the fuel (with fuel cleanser)
Where can I go from here? I'm trying to avoid a visit to the shop, as long as it's nothing terribly complicated to do myself. I may not know a lot about machines, but I can follow instructions.
So...any ideas? I REALLY want to get this thing working.