I have a craftsman 16" 36cc chain saw. Engine

Sounds like it could be seized. Have you been running it on the correct fuel and oil mix? Clutches are centrifugal, so only work when the saw is running, so it wouldn't effect the starting. You would have to have the chain brake on and for the clutch springs to have gone in order for that to effect the saw starting.

The 3 things needed for an engine to run:
1. Compression (Cylinder, Piston, rings, gaskets)
2. Ignition (Spark plug, ignition module/coil)
3. Fuel (Fuel lines, Carburetor, gaskets, bad fuel)

More than Likely I would start by checking fuel related since that is usually the biggest offender (fuel lines broken/dry rotted, bad carb.)

The compression has to be at minimum 100 PSI for a 2 stroke. Some will run under 100 PSI. Turn the screws all the way in very gently and back them both out 1 full turn. This will at least get you started.

Walter:

gently run the fuel and air mixture screws on the carburetor all the way closed (clockwise).then turn them out one and a quarter turns each. That setting should allow the saw to start if you are getting fuel to the carburetor. Once the saw starts, make fine adjustments to the fuel/air mixture screws until the saw runs to your satisfaction.

a chain saw has the oil mixed into the gas if it is not mixed right it will smoke that is the only source of oil to the engine mix up a new batch of fresh fuel and oil mix it will be fine

It is running lean, they always need to run a little on the rich side free running, once the engine is loaded it will then need the excess fuel, it runs ok without the bar and chain because there is no load, start by replacing the fuel filter in the fuel tank, check the fuel hose up to the carb for signs of fuel leakage, replace if reqired, if the carb has standard adjuster screws, increase the H screw by 1/4 turn out ( anto clockwise ) this will richen the mixture.

Take the bar off and clean the grove out with something like a small flat blade screwdriver.Make sure its open where it bolts on.It gets its oil through the bolt holes.If you have a way to blow the dirt out it helps.You can try running the saw without the bar on to see if its putting out any oil.If not you will have to get to the oil pump to see if its not bad.

Turn both jet screws CW to stops (lightly), then back each out CCW 1-1/2 turns. This is a basic setting and should allow the engine to start and run. Start the engine and allow to warm up, then pull the throttle full on. Turn the H needle CW until the engine starts to speed up, but still 4-strokes. Correct adjustment is when the engine 4-strokes running free, but immediately 2-strokes when cutting. Release the throttle and adjust L needle so that the engine idles fairly well, but allows the engine to 'follow the throttle'. Adjust idle speed screw so that the chain stops turning, but the engine continues to run. Hope this helps!

Check the fuel filter for plugging and the condition of all fuel lines. Make sure that all carburetor fasteners are tight. Check the air cleaner and muffler for any plugging. Make sure to warm the engine up before accelerating it. If still not running correctly, try turning the H jet needle about 1/8 turn CCW, which should cause the engine to 4-stroke at speed when NOT cutting, but immediately 2-stroke when you are cutting. Hope this helps!

Steam vacuum? no clue but on your chain saw make sure you check the choke. it would explain why it wouldn't start again.