Put the old spark plug back in. It's possible the gap in the new spark plug is set wrong. Basically, return it to the state it was in where at least it started.
After it starts (but won't keep running) keep pushing that button every second or so - get in a rhythm that keeps the motor running. A minute or so of that might be enough to get it going again. Alternative, after you get it started, keep priming that button the same way, but find a second set of hands to take off the air filter & spray some carb cleaner down there.
If you've thrown out the old plug, then attempt to get it to start using a can of starting fluid. Be careful, that stuff is VERY flammable.