Can you actually access the TC disk on the computer?
If not then you can manually mount the TC in finder and see if TM will then work. Maverick did the usual apple breaking of things.
In the top menu of finder.. Go, connect to server.
type AFP://TCname or TCIPaddress
You will then be asked for a password... as long as the TC is accessible. If you changed the password from default use it otherwise it is public.
If that fails use
SMB or CIFS as Apple decided to break things.
Aint Apple just fun.