Cub Cadet LT 1018 Trans issue

Ok people, I know I'm new here, but I have a major issue, I have a Cub Cadet LT 1018 that had a 31C707 engine on it when I got it instead of a 31Q777, lie its supposed to have, that motor is done, its on my bench waiting on every internal part until them I have a 18 HP IC Briggs on it running great, deck was a mess so I rebuilt it belts kept grinding down and breaking , so I took a cutting we=heel sideways and a wire wheel and removed all rust from every pulley under it, all was good, Saturday I mowed my entire yard (1 acre) Sunday I hooked up the trailer and it barely moved, disconnected the trailer and it will kinda move on flat ground but up the slightest incline it stops totally
I think its the hydro static drive unit, am I correct? can I fix it or do I have to replace it? if I have to replace it where in NE NC can I get a used one that works dirt cheap?