It is a Briggs & Stratton Murray

Remove air filter. Reinstall the long bolt into the carb throat where it goes if you put the filter on it. If the carb has a choke plate, block it open. Give it a shot of carb cleaner, making sure it has enough gas in the tank. Pull rope. If it tries to start, there is hope!
If no run, try loosening gas cap, or removing it to try to start it. If still problem, check rubber gas line for bad insides, and replace if bad.
If you tilted the mower with the carburetor side down, you will have engine oil in the air filter and it must be cleaned out, or replaced. If all else fails, then replace the primer bulb, making sure you get the right one for it!
HTH: Ruaty J.

Is this a model with the carb on the tank? Model / type # of the engine?

If your mower has a square air filter on the front right side, there is a gasket behind the air filter and against the carb that allows it to prime. It must be intact and in good condition. Otheriwse, the bulb could be cracked.