(I pushed the starter button to start the bike back up & the engine didn't even turn over.)
Does that mean not spin on the starter? or it spins but wont start.
The first one is an electrical fault, were the oil light and lights working, if not check earth connections, battery terminals, the solenoid connections, the plug on the ignition switch and the ignition switch itself.
If the lights were still working, and the starter didn't spin the motor, check the solenoid and starter switch, and the earth connections again.
If the starter spun it but it didn't start it could be both electrical (spark wise) and fuel.
It wont want to keep running trying to idle on three cylinders unless the idle is jacked way up. (watch out if that cylinder comes back online when it has the higher idle setting.)
Run it in the dark and watch for any arcing along the leads or coils, weak spark can have a hard time lighting a denser fuel/air mixture (accelerating)
harder to see but wet plug caps can arc down the inside if they get water trapped in them.
Doesn't hurt to crack the drain screws open on the carbs to check for water, rare but not impossible, it's heavier and comes out first.