The battery wouldn't turn over the motor. I jumped it and thought I was good to go. As soon as I disconnected the jumper cable the mower died. I thought the battery might be shorted so I disconnected the battery (both terminals) and jumped it again. It started right up but again as soon as I disconnected the jumper cable it died. Is this a charging system problem? How do I troubleshoot? Any suggestions? Thanks for your time

Bad battery .
Unit will not run with a bad battery.
Have your battery tested
Most shops will tested it free.
Luck

Thanks DG. I know that old school motors like my 14 HO Kohler will run without a battery. Are you saying that the 26 HP Kohler won't run without a battery?

Yes sir that's what I'm saying.
Luck