If it responds to choke then you are not getting enough fuel or too much air.
With old mowers the most likely suspect is a blockage in the outlet from the tank.
No 2 on the hit list is a blocked fuel cap vent.
Well. The problem is finally solved. THANK YOU BERTSMOBILE1 !!! It was a blockage in the outlet from the tank as you suggested. Before I had checked that though, I had replaced the following on my mower:
Ignition Coil
Fuel Filter
Fuel Pump
All fuel hoses
Carburetor
Ignition Coil
Spark Plug
And with all of the above fixes, the problem still remained. However, I did end up fixing it.
The problem was the fuel valve that comes out of the gas tank. It has a 7 inch tube that is inside the fuel tank and reaches the bottom of the tank. Anyway, that tube was clogged completely up. I removed it all fairly easily. It just had a rubber bushing holding it in. Here's the process to fix the problem I had:
Remove the fuel hose connected to the gas tank shutoff valve
Pulled the valve and tube out of the gas tank.
Just wiggle it as you pull. No tools needed.
Take the valve apart. Just one nut holding the knob.
Attempt to blow air through all the tubes in the valve
No air could blow through, so use a thick wire like a coat hanger and clean the inside of the tube
I noticed a lot of build up and fibrous clogged material (probably 30 years worth of old decomposed grass clippings).
Remove all of that gunk out of the inside of all the metal tubing
Blow air through the tube to verify clog has been removed
Put it all back together
WHAM-O !!! The lawn mower roars to life
I think that the problem is finally solved. It all came to about 20 minutes with a hanger and some scraping out the goo from the inside of a 30 year old metal tube to make a hole for the gas to flow out of the gas tank into the fuel line.
All is right with the world!! Thanks for your help and suggestions everybody !!