I forgot to note that the choke is the auto choke that returns to normal when you press the operator bar. I have read some posts that seem to indicate issues with that feature.

Try removing the air cleaner and dribbling in a teaspoon or 2 worth of gasoline in the carb.
Sometimes, a "prime" for its initial Spring start can work wonders.

Have you actually looked in the manual regarding the fuel shut off? My Honda is what I'd consider opposite of "normal".

Thanks Bill. Yes I found the manual on line to be sure I set the fuel shut off in the right position for starting. Horizontal or CCW. I removed the air filter cover to see if there were any problems. To be honest I am not sure what I am looking for. I squirted some carb cleaner in there and reinstalled everything, I think the same way I found it. Still no luck. Where do I put the gas? Where the butterfly is?

Well, just "beyond" the butterfly.

When I move the auto choke, should fuel enter the carb? I don't see anything going on in there. Could that mean the fuel lines are clogged due to storage? How would I go about cleaning out the fuel lines? Right now I have a full take of fresh gas. Do I have to pour it out if I want to clean the lines?

Do you know how to check for spark? The first thing to check is for spark. If you don't have spark no amount of gas is going to help. Once you determine that you have spark then start working on the fuel system.

If you were to take your spray carb cleaner, spray a burst into the carb venturi and give it a pull or two. If it wants to run even a little bit- you've got spark and enough compression to get that far. Two seconds, two basic needs known.
Bill is right when he says that it might just need a helping hand to get going. Lots of times, the fuel doesn't get drained from the carb bowl. A 10mm gearwrench will easily allow you to remove the bowl nut so you can snap the bowl off and see what you have. Many times condensation is lying at the bottom, plus any old fuel is exposed to air turning things to yuck. You can then put a catch pan underneath, and let the fresh fuel work its way through the line to the carb. If it seems gunky- you may have to go farther. You can try bending the straw of the spray so you can direct a burst up through the tube in the center of the stem where the bowl screw turned into. Put it back together and see what you've got.

Not sure what you mean by carb bowl and bowl screw. Nothing labeled that on the parts list. Are you referring to the Float? There is a Screw Set indicated on the Float. This may be a dumb question but when I remove the air filter assembly the bolts go through the carb and actually attach it to the body of the mower. So I guess I have to remove the air filter assembly but leave it attached by the hose and reinstall the bolts to hold the carb, and then spray some carb cleaner in past the butterfly and try to fire it up? Since it also does not list a venturi on the parts list I assume you mean the throat past the butterfly?

Use this link to see a bowl and the jet. The bowl is in the top picture of the thread. This is what happens when water lays in a carb and/or gas dries up or varnish over a longer period.

http://forums2.gardenweb.com/forums/load/lmower/msg051313339279.html?3

You may just wish to consider having it professionally serviced and not have the worry.

Thanks for the help guys, I got it running. I first tried squirting carb cleaner into the carb and it fired up for a second. Then I squirted some gas in and it did the same thing. So I took the bowl off, but the carb was clean. I squirted carb cleaner everywhere I could, reinstalled, and nothing. I still have to squirt gas or carb cleaner in to get it to fire for a few seconds. But I had an idea and tied a rope to the choke and held it open and then tried and it fired up and kept running. I tied the rope off and let it run about three minutes and when I released the choke, took off the rope, and it kept running but the engine wanted to surge some. It never acted like it wanted to stop, just up and down in RPM's. I mowed a small spot and it seemed like the surging was starting to even out but that might just be my imagination or the resistence of the grass. I stopped and started it a few times and it fires up on a half pull, but I have to use the auto choke as normal or it will not start. I remember they guy I bought it from said he did not have to use the choke to start it so maybe it will get smoother as the season progresses. Anyway, thanks for the suggestions and all of the help.

IF it sat a couple years, there's still probably some gum/varnish, since it's difficult to get 100% of the fuel out of the lines, carb passages etc.

For your first mowing (2nd if not too late), I'd add a STRONG dose of carb cleaner to the tank.
Mow.
When done, top off the fuel and run a few minutes so the "strong dose" is diluted and not eating away at rubber parts etc....in the carb.