The assumption is that the engine started and ran normally prior to the incident. Now, no matter how many times you yank the starter rope or run the electric starter, it will not start at all, bucks, kicks back, backfires, or fails to develop enough power to keep going on its own.
If the blade struck a solid boulder while the engine was set on 'high', more severe damage is possible as even with soft metal keys locking the blade and flywheel to the crankshaft, the inertia of the rotating blade is acting sideways against the crankshaft in addition to suddenly stopping its rotation. This can result in a bent crankshaft. The end of the crankshaft with the blade adapter could be bent without affecting the bearings or internal parts. This would need to be tested for as well. Not that such an occurrence is that much better - the crankshaft would still have to be replaced but at least the bearings in the crankcase will not be damaged.
If the starter will not turn the crankshaft (assuming you remembered in your haste to engage the safety bar) - it is seized or will only rotate part of a revolution before hitting against something solid inside - then you probably have serious internal damage that will require a complete strip down and replacement of some (expensive) parts. If it turns but much more tightly than you recall (assuming you do have the safety bar engaged!) then the crankshaft may be bent - again very expensive. Repair may not be worth it.
However, in most cases, what has happened is that either or both of the blade lock key and/or flywheel key have sheared to protect the crankshaft from serious (and terminal) damage.
If the blade lock key broke, the blade will no longer turn rigidly with the crankshaft and provide the inertia required by many small engines with undersized flywheels. In this case, the engine may try to start but die out with a few "putt-putts" or even kick back on the starter cord. (As a side note, attempting to use a lawn mower engine as a replacement on a piece of equipment that doesn't have something to substitute for the blade's inertia may not work for this reason.)
If the flywheel key broke, the ignition timing will likely be totally wrong and the result may be no ignition, backfiring, kickback, or weak or total loss of power.
To diagnose, proceed as follows:
First, pull off the spark plug wire and tie it securely away from the spark plug terminal (several inches minimum) or remove the spark plug entirely so that there is no chance of the engine accidentally starting. Even though it will not start now no matter what you do, the underlying problem could actually be a flooded carburetor or something else which may correct itself while you are working. Never take chances.
Drain the gas or remove the fuel tank. This will prevent gasoline from spilling out the gas cap vent hole or flooding the engine through the carburetor since you will need to tip the mower to get underneath.
Set the mower on its side (carburetor side up).
CAUTION: Immediately check for oil leaks at the oil filler pipe or elsewhere.
The mower can usually be set on its side for a few minutes without harm but if these occur - you will have to work with it tipped less than 45 degrees or so - propped on wood blocks. Or, use this as a good excuse to perform an oil change and drain the oil (even if the engine is cold, most of the oil will drain out - it will just take a little longer). Just don't forget to refill the crankcase with fresh oil once you have completed your work!
Using an old rag and/or proper work gloves, grasp the blade and attempt to rotate the blade and crankshaft.
CAUTION, despite your lack of maintenance, the blade may be sharp!).
The blade and crankshaft should rotate together. If there is slippage, the key has broken and will require replacement of just the key or the entire blade adapter plate depending on design. If it appears to be intact, then you can assume the flywheel key has broken. The blade key may be broken as well but it is not likely the reason for your failure to start. You should remove the blade to determine this for sure before restoring the mower to service in any case. See the section: Non-violent blade removal.
You can possibly avoid removing the flywheel for inspection of the key by unscrewing the sparkplug, rotating the crankshaft so the piston is at TDC, and noting the location of the magnet on the flywheel relative to the magneto coil pole pieces. The magnet should be pretty close to the magneto in that position. If this is not the case or just to be sure, the flywheel will have to come off to inspect and possibly replace the key.
To get at the flywheel key itself, some disassembly is required.