murray riding lawnmower will not start
"Still sounds like a dead battery...."
Skymaster has good advice. Always start with a well-charged battery.
Can you identify where the clicking sound is coming from? Sometimes sounds can be confusing. It could help to disconnect sections between the battery and the starter to isolate the problem.
Also, there is probably an inline fuse.
Just to mention- the starter is part of the engine, not the lawnmower as such. Go to any online lawnmower parts dealer and you should be able to look up the starter if you need to. Or, just take the starter off and look on it.
If it's worth doing, it's worth doing right. If you wouldn't put your name on it, it ain't done right!