More than likely it is the beat up air filter..... But there's something
that might be so obvious that you may have missed it..... Check out the
gasket between the carb and the air filter.....(That's one of my
favorited stunts, is to neglect to put it back in after I'm done
cleaning the air filter). And make sure the 'rubber boot" between the
air filter and carb doesn't have a hairline crack in it....
If it's air being pulled through a crack, it'll make it hard to start,
and it'll almost refuse to idle. And you might consider a carb rebuild
kit.... It'll run you about 25 bucks...