I worked at a Mower shop once upon a time.
Odds are good you didn't break a rod
My view always was Look at the mower ask yourself what would I pay for this at a yardsale/auction etc. Forgetting what you know about how well it has been cared for. Use this number to determine how much you want to spend on it. As for checking it out.
remove spark plug lead
Tip mower on its side, carb side up. Enough you can see under it.
Have someone pull it thru or engage the starter
watch the bolt that holds the blade on, if it wobbles the crankshaft is bent and the mower is junk -- cost to repair will exceed the value of the mower
If ok
check sparkplug to be sure it is tight
check head bolts to be sure they are all tight you should be able to get a feel without a torque wrench.
Check for spark,
remove the plug, plug it into the lead, touch the plug to the head and pull thru to see if you have spark.
Next, place your thumb over the spark plug hole and pull thru. It should blow your thumb off the hole indicating you have compression
Beyond that it is probably a flywheel key, which times the engine.
remove top cover
remove the rope starter cover
remove the large nut holding the flywheel on
get 2 prybars and remove the flywheel.
replace the $.69 key with a new one
reassemble
If you need any parts at a mower shop you will need the make model and serial number of the mower and the engine.
Mower info should be on a sticker usually on the back of the mower
the engine info is generally on the top cover of the engine. on the front stamped in or over the muffler stamped on a plate.
Partstree.com is where many mower places get their parts, if they are not a Briggs repair shop. you can buy there to for the same price.