eton challenger 150 won't start/cuts out?

I recently bought a Eton challenger 150cc off eBay. When I got it home it was very hard to get started,but I eventually did it. We then rode the bike for around 1 1/2 hours on and off but it started every time. I must add to get it started I hooked a battery up to the wires to attempt using the starter motor, but I think the starter is shot. We then kick started it but it still would not go, but only until I took the battery off it started.

The next day it would not start without using the battery to kind off charge something in the electrics. We rode it for 20 mins and then it cut out, I started it again and then it cut out again 10 mins later.

I have concluded this:
Engines getting fuel.
Kill switch works.
Vent for fuel cap is clear.

I just want some advice on what could be causing it to not start and cut out.