Having a difficult time starting engine. I tried with the choke all the way out, and the throttle shut down, I tried with the throttle half way open, and the choke half way out, and I can't get the engine to start. When I had the engine running before, I couldn't get any pressure out of the nozzle.

this could be a few things as to cause :

1- throttle cables stretch as they get older , if marking on throttle says "run" it might really be choke on carb - looking down carb body(air clean off) with engine off move throttle to choke the choke butterfly should shut off (choke does have small hole in it) the butterfly should not be just barely moving or half way it needs to be closed all the way
2- modern fuels leave deposits inside of carbs if machine is left to set for long times (weeks) these deposits don't just get washed away when the engine is started again either , they must be chemically or mechanically flushed away by either a carb cleaner (chemical) or taking carb apart and cleaning it totally out (inside and out) -these deposits cause poor carb performance and even non working engines
a method to keep from having to do this often , is to install a fuel shut off valve in the fuel tank ( might already have one there you just gotta look for it) and when your done with machine shut off the gas valve and allow it to run out of gas dry !

Are you sure it's not a new style Briggs that uses the 'throttle cable' just as a shut off? Many new mowers on;y start and run at High Speed

Bowl float is sticking open.
Turn the fuel on tap the carbbie bowl. With something ie end of a screw driver etc... your trying to get the float to unstick. Before you put it back together. ..ie putting the bottom on make sure the float goes up and down freely

Full choke, stop switch on run. Pull rope handle 3-4 times or more until it "tries to start" (it will not start, but it will try to for a split second) move the choke lever to the half-choke position and without pulling the throttle, poll the rope handle until the engine fires and runs for 4-5 seconds then fully open the choke to the run position, let it warm up for 25-30 seconds (don't forget to let it cool down about 45-60 seconds before you turn it off!) and then proceed to use it.

The choke system is connected to the half throttle position, if you lift the throttle trigger the choke pull will automatically return, whilst trying to start do not lift the throttle trigger, the starting procedure is, pump the primer bulb as many times as it takes to 3/4 fill the bulb, pull the choke pull fully out, this will switch the saw on and engage the half throttle, crank the engine until it fires once, do not continue to pull,it will actually not run on full choke, if you do continue to crank with the choke fully out, you will very quickly flood the engine, now push the choke fully in, now crank the engine until it fires up, lift the throttle trigger once, this will dissengage the half throttle, and it should now come down to idle.

Most LR 10 i saw were fitted with a Briggs and Stratton engine, there is normally an in line fuel filter from the tank to the carb, this may well be part blocked, so start by replacing this filter, make sure the fuel in the tank is fresh and clean, make an adjustment to the throttle cable, with the air filter removed you can see the choke flap, make sure the choke flap is closing fully as you move the throttle control on the dash board to the choke position, also make sure the choke opens fully in the full throttle position, there is a single screw which allows you to move the cable in or out to achive the correct opening and closing.as the filter is now off replace it with a new one, now try again.

Don't prime it 6 times.

Prime it once and try starting. Keep trying with one prime.

If that doesn't work, let it sit for a bit. And then prime it two times and try starting again.

If that doesn't work, try priming 3 times.

Then try half-choke with one pull only, and then move choke to run for the second pull.

The saw might have an on-off button

The choke actually just opens the throttle bodies a little (the bike is fuel injected). Try using putting on the 'choke', then pressing the start button, but dont touch the throttle. Does it start ok? Also, when started, if you use the 'choke' does it increase the engine speed? If it does not, then you need to set it up correctly.
Let us know how you get on.

I have 2009 lawn tractor that will not start (from day 1) unless I use a small squirt
of start fluid into the air cleaner area. Nothing else seems to work. The battery will run down before it starts. Once engine is warm it starts great. Love the tractor,
hate the starting problem. Elevation is not a problem in michigan.

Shut off fuel to carburetor, drain carburetor. Open fuel and count to three then shut off fuel. Crank engine then pull choke for 1 second then push in. If engine starts open fuel valve at tank. Also try lowering float level in carburetor. Good luck.