I
had a gold LT3500 that I bought new in 2008.
Do you have any leaks at the rear axle seals ? Mine did right after warranty (naturally) it had a POS Dana made in china transaxle. The whining sound I experienced was due to low on gear lube. I was able from time to time remove the battery & drive pulley & the transaxle had a rubber fill plug. But only held 10 oz of gear lube. So didn't take much to be low. I would add s few ozs' of the thickest gear oil I could find. (temporary solution).
I later transplanted in a Husqvarna transaxle & it was good. Mine was a 6 speed tho, not sure about yours ?
The owners manual (if you have it) will list the transaxle type in it.. if not you can go to
www.SearsPartsDirect.com , it will allow you to type in your model # & it'll show you schematics of every part in your mower