Honda Elite 50 died mid ride?

So I was riding my honda elite 50 scooter yesterday and out of nowhere, the scooter just turned itself off and I coasted to a stop. This has happened once before and the last time it happened, it was due to lack of oil in the gas. The scooter is a 2 stroke and needs oil mixed but has a separate tank for it. Last time, the tank was empty so I assumed I just hadn't put oil in it in a while but when I checked the tank this time, it was still half full.

Electric start won't do anything but kicking it sounds like it wants to go. It was pretty cold yesterday so I don't know if that would do anything. Could it be the battery or maybe just the spark plug?

I hope that the last time it stopped, it was because the safety switch shut it off, and not because it actually ran out of oil. Once it starts, the cold temperture outside should not effect it. It would be good to get it inside for a few hours to warm it up for the next starting attempt. Charge the battery, make sure the terminals on the battery are clean and re-attach and tighten. May as well clean (or change) the spark plug, because that is bound to help.

Other than that, it could be any number of things.

From previously running without 2 stroke oil, the piston & rings would have started to ware out.
Maybe you caught it in time to prevent any major damage.
This time it sopped running because the slight ware from lack of oil last time, the piston & rings only had a little bit of life left in them and wore out completely.
Check the cylinder compression.

Get a tune up first. Clean the carb.