Looks pretty much like my boys bike tbh, maybe slightly nwer mayber slightly older, but either way cheap Chineese thing
Anyway the bit you want to know, why wont it start
Two things, my boys was running fine then just got harder to start untill eventually wouldnt at all
Went through everything

and turned out was hust the petrol had gone stale

, (he didnt use it much lol) where it had just stood.
Just drained it all out and filled with new fuel and was fine (was always relitivly easy to start, BUT be carefull with the pull cord as they have a habit of breaking apparently, done one on mine and now start it "correctly", ie pull the cord slowly untill resistance felt then sharp pull up, but not to big a pull the cord aint that long and will damege mrchanism if pulled too far)
AND now the IMPORTANT reason why it may not be starting, I think that wire of yours comes up with the HT lead, mine got a cover on so cant see exactly where it goes (and to take that off means taking all the starter off as well and dont really want to go there tonight

) BUT if it is this wire from the coilish area, it is the engine KILL SWITCH WIRE ie once the bike running u GROUND this wire to STOP the engine, so if u have it grounded dont think u are gonna have a lot of luck
If u was to post a pic of the wire would be helpfull
Steve