You've got a Ignition System Issue which narrows things down quite a bit. It's either the ignition switch that your key goes into, or an on/off(run/stop) switch, or it's a relay for the ignition systems(or starter relay), if it's none of those then it's the starter solenoid that you've been jumping with the screwdriver, it sounds like the starter is working as it should since it turns over- the reason it turns over but won't actually run is because the ignition system won't work unless the key is inserted and in the run position, or if there's any other on/off switch that controls your engine it could be there. I'm not familiar with this exact bike but this is a common issue with all motorized machines! You can bypass all of this but that requires running some wires and a couple of switches plus a relay or two- that's an option but don't do that as your issue is nothing major and would be easier to fix than to go through the trouble of re-wiring it all. Just start troubleshooting and eliminate one part at a time, check relays, fuses, and electrical connections first, then the individual components I listed above and check to make sure they have power coming in and out when/where they're supposed to. If your bike turns over but won't run and the key is on, and you have a functional Ignition system then you need to verify you have ignition by checking your coil's output. EASIEST way to do so is pull a spark plug and connect it to the spark plug wire as you normally would, then hold the spark plug against the engine to ground it and turn it over- you'll see if you have any spark jumping aroundbetween the spark plug's electrode and the base of the plug itself. Either way, you'll get this figured out now that you know where to start and what to check!
