Briggs Straton 13.5hp Poulan Mower won't run with

The lawnmower used to run fine, but on occasion, after an hour of mowing (level land), it would sputter and die. Starting it again required the choke to continue running.

Now everytime I start it, I need the choke on completely to keep it running.

I cleaned the air filter and sprayed in some carb cleaner, but it didn't help.

If it needs choke, the only thing I can think of, is that the carb is getting air from someplace else. If that's the case, how would I find it?

Is there a possibility that the tank does not have a gas cap vent? There's a cap, but no vent hose coming out of it. So I tried starting the mower with the gas cap loosened. It still didn't work.

I was a little nervous about removing the carb, but went ahead and did it anyways. After carefully noting bolt locations and attachments, I got it off the tractor and into the garage. It seemed ok in the main tunnel (not sure what it's called), but once I removed the float bowl on the bottom, I found a large buildup of rust and mud. I cleaned out the bowl and sprayed a carb cleaner through the smaller tunnels until no more mud dripped out, then blew compressed air to dry it up.

Then I reassembled it, and turned the key. At first it wasn't firing (which makes sense..the float bowl needs to fill up). Then it started to run, and died after 4 revolutions, or so. Now it won't even run with the choke! I can get it to fire 4 times or so, then immediately after it dies. And I even killed the battery trying to turn it over enough to start.

What options do I have left over? Do I have to get a new carb?