Need advice about problem with my Sym scooter please

Hi, really hoping somebody can help me, i've recently bought a Sym city hopper 50cc scooter, it has a full MOT on it (done a couple of days before I bought) so hoping it's not a massive problem or it would have been detected i'm guessing. It had been stood a bit so the guy said it will probably need the battery charging as electric start wont work, but works fine off kickstart.

I took it out the day after and did 12 miles fine, started first time setting off and from the shop and petrol station, so 3 times starting and all ok. Gone to start it yesterday and its dead. Have bought a charger and made sure it's the right one and left it on charge overnight (13hrs in total). The electric start won't start still, but does sound a LOT healthier than before and as though it is almost starting. Kickstart is completely non-responsive and after about 50 attempts and hurting my foot, i've given up! The indicators, brake light and hazard lights all come on perfectly fine, but the headlights won't work at all, and the scooter won't start.

Am I looking at an electrical fault or is it probably just the battery that's knackered and needs replacing? Is it normal for all other lights to work except headlights/rear light? Any help and advice is very much appreciated!! Faced with £20 in a taxi home from work every night if I can't sort it soon

 

Headlight wont work until it's running. Forget about the mot, that means nothing, try a new spark plug and there might be a knack of starting it.