To reinstall your push rod you can loosen the jam nut on the adjuster. back off the adjuster then you should be able to move the rocker to the side and install the rod.
If its one of the end rods you can remove the hair pin clip.
Try turning the engine over by hand with the fan.
A carb rebuild is a good idea, disassemble it this time. After soaking the removed parts in carb cleaner blow air through all the passages.
