My mother inlaw has a JD riding mower that's about 8 yrs old and has been in the weather for about the last 6 mnths, and it won't stay running unless I put the booster cables on it and jump it from my truck. It will run as long as they are hooked up but the moment I disconnect them it [the mower]dies.Is this a battery or charging system failure? I have used a trickle charger to charge the batt. But I have the same outcome.Thanks for your help.

Replace the battery, It right now just sounds like a lifeless battery.

The thebriggsdude is right. Go to walmart and buy a lawn mower battery for it.