The top gasket around the float bowl does not have to hold pressure - it is there to keep fuel from slopping out when you run over bumps or work on a slope. It looks more squished than torn or chopped. However it mustn't leak - loose fuel around a running engine is dangerous, especially when it's right under your backside. The safe way to go is to reassemble the carburetor, fill it with fuel, and try a bit of shaking and tilting to see if liquid fuel leaks out. Then, either before or after putting the carburetor back on the mower, turn the fuel on with the carburetor the right distance below the fuel tank, and fuel in the tank. Wait ten minutes and see if it floods, drips, leaks etc. If it doesn't emit any fuel, it's time to crank up the engine.
Do you have the owner's manual, to find the correct way to start the engine (use of choke, etc.)? Old Briggs engines are very easy to start if everything is working and if you follow the manual. Does it crank at a sensible speed? Some of the larger Briggs engines have automatic decompressors, and if they don't work the engines are difficult to crank, overheat the starters, ruin the batteries, and sometimes cook the wiring.
