Buy yerself a good trickle charger for the battery. Charge the battery for 12 hours or so. See if it'll start. If yes, then wait a week or so, until you are sure the battery is ok. If not, then, if the battery is more than 2 years old, it might be time for a new one. Those lawn tractor betteries are usually good for 2 years of use. anything after that is a crap-shoot!
The problem is: With the safety regs in place for everything--as soon as you move yer butt off the seat, the engine stops, and then you have to restart it to continue on. Every time you re-start the engine, a bit of lead leaches off the plates/grids in the battery, and shortens the life of the battery! You can charge the battery, but an old one will get a top charge, but give out shortly as you try to re-start the engine! BTDT! RJ

There are a couple of things that could use clarification. As far as the quality of the cranking, is it cranking fast enough? Are you getting a partial crank and then the engine acts as if it is too hard to crank further? Or are you getting a simple click from below the seat and no cranking?

usually when it dies, it just clicks and then eventually just does nothing at all. Yesterday I could hear the starter turn over but no spark, then it went completely dead....Battery is new...I"ll charge it up the next time and see what happens...thanks for the replies.

Ya know I had the same thing happen 2weeks ago. Well almost. I didn't have a corroded wire. I've a good manual I bought in pdf format. Turned out to be the Solenoid.

{{gwi:337272}}

$10 later I was mowing!

Good Luck!

It sounds to me like the battery isn't being charged by the engine.

However, IF you think you have a parasitic drain, disconnect the neg. battery cable when not in use and see if the battery stays charged.

Just because a battery is new doesn't mean it's good.