I would suspect that you are not getting all of the bubbles out of the gas lines. Don't worry about the 10 strokes, prime until there are no bubbles showing in the lines to and from the carburetor. Any bubbles in the lines restrict the fuel flow.

I have primed after the motor has started, and I see a bubble. You can hear the change in engine speed as the bubbles are cleared from the lines.

I find that I get the best prime by not just pushing the priming bulb, but push it IN fast, and then take your finger off of the bulb and let it expand slowly.

If it does not start with in about three cycles, stop and wait a while as you do not want to flood the engine.

1. Is the fuel fresh, ethanol treated with Stabil or a stabilizer if so?

2. Check all fuel lines for air tight fits.

3. Can you see airless fuel moving when you are priming?

4. Try starting with the air filter off and look for signs of fuel while priming.

5. Add a little premix to the carb as a Manuel prime if no fuel is noticed at wide open throttle.

6. Check for a good blue spark, with the plug grounded, ignition in the on position, cranking.

7. Check other related post for Ideas!!!

1. Is the fuel fresh, ethanol treated with Stabil or a stabilizer if so?

The lady said this was a 4 cycle so there would be no problems with the triple point of the alcohol, gasoline and oil mixture changing so that one or a combination would drop out of solution.

Pure gas or gas and alcohol evaporate cleanly with minimum residue (less than 0.1%), unlike a 2 cycle that on evaporation leaves a bout 2% residue (50:1 gas/oil) remaining to clog up the system.

I would advise the OP to ensure that Ethanol fuel has not fouled the carb. If the unit has not been properly drained or treated since the beginning of summer than even Non Ethanol sour fuel would certainly be a factor to consider . It does not take much varnish or debris to restrict the Main and Primer fuel circuits within Troy-bilt carbs.