Well, ZK-KCBB-3K5A-2WLX is a valid transmission code, which leads to an Illustrated Parts List, and the IPL seems to be identifying it as a ZT series transmission:
http://www.jackssmallengines.com/Jacks-Parts-Lookup/Manufacturer/hydro-gear/3571/3223

You can download the ZT service manual (free) here:
http://www.hydro-gear.com/Main/docs/service-repair-manuals/zt-2800-3100-3200-3400.pdf

I suggest you look closely at that manual and see if it covers your transmission.

Aside from that, you said it isn't driving, forward or reverse. Do you mean that wheel will not rotate? The reason I ask is this extract from the ZT manual:

"The ZT-2800, ZT-3100, ZT-3200 and ZT-3400 have an internal cog style parking brake. It is essential to fully disengage the brake prior to operation."

Usually, warnings like that in a service manual suggest that this may be a common source of trouble. If you have a cog style parking brake, and it is not fully disengaged, that wheel isn't going to rotate much.