JD 3032e won't start after battery charged

[OneMan]

Went out to the property today and found that the light switch had been left on and drained the battery completely. After charging it, the JD 3032e wouldn't kick over. It seems that the starter doesn't want to engage. It clicking sound associated with a dead battery is there but the engine won't kick over.
Took the gas filter out the inspected it but it was clean. Took the battery out and hooked up the cables directly to the tractor cabls but still no start. Tractor only has 55 hours on it.
Problem is the FEL can't be raised or the brush cutter either so I can't pull it or load in on the trailer.

Any suggestions besides a call out mechanic from 36 miles away?

 

[Willl]

Battery's toast, replace it.

Jumpers can't handle cranking current by themselves.

 

[OneMan]

Battery's toast, replace it.

Jumpers can't handle cranking current by themselves.

Any hints as to what type of battery to buy?
My owner's guide says a 500 amp cold start 12 volt battery.
I didn't think they made a 500 amp battery.
Where to buy one?

 

[Willl]

Lots of arguments on battery flavor.

I myself run Interstate in my truck and a Optima in my JD.

Do a "500 cca battery" search in Google and pick your favorite.