You should at least get some sparks or something if you're shorting across the 2 biggest solenoid terminals...
Test the battery voltage when you have the key in the start position, congress hasn't passed a law yet saying 1 year old batteries can't go bad

Another test on here that i stole from Bert,
Get a set of jumper cables, hook to the battery, + to + - to -.... hook the other negative end to a good ground, unpainted bolt, etc, then touch the + lead to the starter + terminal,(expect some sparking), if the starter turns and it cranks normal, the battery and starter are good, and there is an issue with the wiring, either in the trigger circuit/mower wiring..
if it does not crank like normal or nothing, i would conclude the battery is kapoot.
O'reilly auto parts and most parts stores will load test a battery for FREE.