The first thing I would check is the fuel solenoid on the bottom of the carb. With one hand gray this solenoid and with the other hand turn the key switch to the run position, not start. You may need an assistant if your arms are challenged in length. When you do this you should feel and/or hear the solenoid click. If it does the solenoid is working. If it doesn’t click, the solenoid is stuck or not getting power. To check for power disconnect the solenoid plug and test for 12 VDC with a test light or VOM. If you have no power take a jump lead an jump the solenoid from the positive terminal on the battery to the solenoid lead. If it still doesn’t click the plunger is stuck. You will have to clamp off the fuel line to the carb and remove the solenoid. Since you don’t tell us the brand name of the engine or all model and serial numbers, I can’t tell you how to remove it. If it is an older Briggs you may have to make a special tool. Post back after you’ve done your tests.