Push start can be done even without any battery inside the bike. I done a video on this before with the battery placed on the pavement before I push start.
Is there a cranking sound when you press the ignition button?
If have, then it is not a battery problem.
If there is no cranking then it may be a battery or wiring problem.
Cannot start can be because of many factors.
One thing I can think of is someone itchy hand play with your bike and the carb is flooded. Or after 1 month, somewhere somehow rain water went in.
Try this. Off the fuel c0ck, drain out the carb using the drain screw, tighten the screw after draining. On back the fuel c0ck then push start.
If it is not an electrical problem or a fuel problem then it might be the spark plug. Ignition problem.
Hope that helps.