What's wrong with my lawnmower?

[xoxoxoBruce]

Three things, spark, fuel, and timing.
First thing is to see if it has spark at the plug.

...using the key to start it results in absolutely nothing happening

Nothing as in it doesn't turn over or it doesn't start?
Pull the wire off the plug and see if the spark will jump a small gap between the wire and plug when the engine spins.

Second thing is fuel. pull the spark plug out and spin the motor over a few times. Do you smell fuel? Will a match to the plug hole make a small flame? If not the fuel from last year has probably turned to jell in the carburetor and needs to be cleaned out.

If you have spark and fuel take it to a pro for repair.