It probably needs a new diaphragm.
Part Number: 270026
DIAPHRAGM-CARBURETOR
US$ 2.05

Go to the Briggs website and download the IPL for your engine for an exploded view of the carb.

I'd get a can of carb cleaner and use the plastic spray tube to blow through the 2 holes under the diaphragm.
One will vent into the carb venturi and the other through the fuel pick up tube in the tank.
It's usually easier to remove the muffler to have a straight shot at the screw heads to avoid stripping them.
Watch the spring when removing the diaphragm cover

http://www.briggsandstratton.com/maint_repair/manual_and_more/.

did you turn the shut off valve to the off when you drained it and on position when your wanting to start it if your model has one?

If so I would make sure gas is getting pass that I would also take the hose off at the carb and make sure gas is getting to the carb.

Prime it by removing the spark plug, clean it, check gap, and spray some carb cleaner directly into the comb chamber. Usually a two second blast is enough. reinstall the spark plug and fire it up.

If you don't want to fool with removing the spark plug, remove the air cleaner and spray 3 to 4 second blast of carb cleaner into the carb. venturi (hole or opening) raise the throttle and choke it. it should suck the carb cleaner down and fire off it. This will usually move the trapped air in the carb. and alow the gas to start flowing visa vacuum suction effect. You may have to do it a couple of times or squirt enough carb. cleaner into the carb to keep the engine running long enough for the fuel to flow.

If that don't work Then I would think about tearing the carb. apart.

Need a exploded view of carb for springs and rods on a craftman model 917 298350 5hp front tine tiller have a basket case