The older DTSs (2004 DTS for sure) can be programmed from the existing remote. Some time after 2004 (at least by 2008) the built-in GDO remote could no longer be programmed from the existing remote. If the GDO is old enough to not use rolling codes, the car has to be programmed to the same switch settings as in the existing remote. However, it is also possible that the GDO could be so old it uses a different frequency than the car, and the car cannot be programmed at all to work with the the GDO. In that case, you need to get the adapter I got (see post #7 of this thread) to make it work.

Just for informational purposes, I have always been able to program the car from the existing remote on all my CTSs. This includes three models from 2004 to 2009. Newer DTSs apparently use different built-in GDOs than CTSs .