Your problem is
likely due to excessive voltage drop across the various 'safety' interlocks...
That has been a problem for John Deere and other manufactures for some time... So they came out with a relay kit to help with the problem...
If you do not already have it on that mower, you need to put one on... You can make your own for around $10 or buy it ready to install for around $25 to $30...
Here is one on eBay :
John Deere Starter Relay Kit Lawn Tractor Rider Part | eBay
The interlock switches are the actual problem... but with this relay kit, you can get by using the bad switches that were used by the manufacturer.... :smile:KennyV