That's an inverter style generator......a chinese copy of the Honda EU2000i. The ignition coil doesn't sit next to the flywheel, as you see in the close up photo of the coil. Instead, there is a trigger unit mounted next to the stator ring, and that supplies the pulse that causes the coil to generate spark. Blue is probably the signal wire from the trigger, and yellow is the kill system wire, which is grounded by the oil level sensing system and/or the on-off switch.
Firstly, change your oil. Low oil level and extremely dirty oil will trigger the oil level sensor, thus killing spark. Once you have clean 10w-30 oil, filled to the edge of the threaded oil fill hole, retest for spark. If you have no spark, report back. And just an FYI, old dirty engine oil in these, and the actual Hondas, rots the timing belt, causing it to break. It is a complete tear down of the generator and the engine, in order to replace that belt.
Also, let us know what make and model that thing is.