I've had to replace a few fuel systems on older machines - something to check.
From the left side on the machine, look up into the carb - you will see a little screw on the bottom of the carb. CAREFULLY turn it counterclockwise 2 or so turns - this drains the float bowl, so be sure you are outside or prepared to deal with the gas -
If any comes out.
#1. Gas comes out - Let it drain, leaving the valve open, turn the key on (do not start it, just turn the key on!) and listen for a clicking/ticking sound - that is the fuel pump. It is under the gas tank, towards the back.
The bowl should start to leak again as the fuel pump pumps gas to the carb -
If not, well, you have a problem in the fuel system . See #2
If it does pump gas out again, close the screw CAREFULLY - DO NOT CRANK IT TOO TIGHT!!!!! and see if the machine will start - more times than not, I have that fix it - fresh fuel in the bowl, vrooom!
#2 - no gas came out and none came out when you turned the key on - You have a fuel system issue IMO. I'd replace it all, fuel pump, fuel filter, check valve and hose, but that's me. Last one I did I cost the owner around $180.00 (I think) for everything, parts, labor, fresh gas, "shop supplies" and tax.
You can do it yourself for a lot less, and it is a great time to check/adjust those valves.
Oh - if you are getting fuel and all that is good, well, you have some other problem!