It would be helpful if you would post the actual engine Model number and Type number found on the engine itself.
But yes, your next step should be to remove the spark plug and check for the presence of compression on the non working cylinder.
It is simple enough and effective enough to just place a thumb over the spark plug hole and see if it has enough compression to force past your thumb and escape when you operate the starter.
Be sure you move the spark plug cable far enough away that you don't inadvertently check for spark as well (shocking).
If you find that the cylinder has no compression, your next step after that will be to remove the valve cover from that cylinder and look for a pushrod to have fallen out of place.
I think that is enough for you to work with for now.
Report back as soon as you know something.

Also, when you remove the valve cover-
IF everything looks good, rotate the engine by hand and see if both valves have the same amount of travel.
Some of these are known to "eat" cam lobes.

I think you meant LT 2000?
In my homemade Sears database, all the LT 2000's I have are single cylinder.
Could you post the Sears 917.xxxxxxx number please?

This post was edited by bill_kapaun on Sun, Nov 10, 13 at 8:16

Mea Culpa! Yes, it is an LT2000, not 200. And the Sears # is
917.275520, engine model B&S 445577.

I was able to narrow the problem down to fuel: it not only has spark (and compression) in the right cylinder, but will run on the right side with the choke full on. Shut off the choke and it will run for a few seconds, then starve out and shut down.

I changed out the fuel, thinking it might have something to do with 'bad' gas, no such luck. Still only runs on the left cylinder. So it must be something gunked up in the carb.

Very good work there! :^)
Be very careful if you undertake to dismantle the carb for cleaning.
Be sure to label all your parts and take pictures as you go for reference later.
There is a left and a right main fuel jet and they are not interchangeable.
Most likely the jet for that cylinder is gummed or has trapped a piece of crud in it.

Good advice from mownie-

I'd also suggest going to the Briggs website and downloading the IPL for your engine (445577-0485-E1)

It'll have some exploded views and current part #'s.

In some cases you get by cleaning the pick up tubes from the top. Light air pressure is ok, no carb spray. Like with the the air down to about nil or use an air can as to not dislodge the main jet. You may end up cleaning it anyways.You can also clean these by pulling the lower control aside and removing the bowl if you are set up to do it. Many of the seals are available separately should you need them rather than buying an expensive kit.

This post was edited by tomplum on Sun, Nov 10, 13 at 21:33

Thanks for the responses. I'm pretty comfortable with removing and cleaning the carb, do all my own motorcycle maintenance. I will probably try removing the bowl first but will download the diagram from B&S first.

Thanks again!