I don't use Sybase, so I can't test these recommendations. I'll take a shot for you, though.

My first guess is that you need to use CPAN or such to reinstall DBD::Sybase.

My second guess is that you need to install or reinstall the client libraries upon which DBD::Sybase relies to connect to the database.

When the error says that the module cannot open the shared object file libct.so it means exactly that. The DBD is looking for the library somewhere it can't be found. It's not present or it's somewhere other than the module expects it to be.