Google: Cub Cadet Professional Shop Manuals, scroll down page for LTX , see wiring schematic. If you're not sure about battery being good or bad, remove battery & take to any auto parts store for load test.
See page 142 item 2 in manual for no power. As for transaxle problem check for brake adjustment in manual pages 62 & 97 depending on type your tractor has. Also I will suggest you remove both rear wheels, one at a time using jackstand under frame & front wheels chalked or scotched, & apply anti-seize compound to axle shafts liberally, this will prevent wheel seizing to axle shaft. You can purchase anti-seize compound at any auto parts store in small packet form inexpensively.
Wiring schematic is page 198.