04 deville. Trans is stuck in gear. Or seems to be. Car is off. Crank car, starts fine so gear selector/neutral safety switch is ok? Car is running, shifter is in park, take foot off brake amd car moves forward. Since its in gear. Apply brake, shift to neu or rev and car will still move forward. The 2000 caddys had an external neutral safety switch. The 04 cars have an internal switch. If that has an bearing on discussion. Could trans shifter linkage inside trans be messed up? So spool valve in trams is always in gear but shift selector works properly so car can be started?
Bad shift solenoid http://etereman.com/blog/general-motors-transmission/beware-common-problems-of-the-4t80e-automatic-transmission
4T80E
The transmissions above are 4 speed automatics that are computer controlled. The most common problems are: Your check engine light comes on. The transmission starts shifting erratically or not at all. Make sure you or a shop runs a scanner on the vehicle. You want to see if a sensor has gone bad causing your problem.
Ask your shop to do a visual inspection of the linkage between the shift lever and the transmission, checking for broken linkages, etc. It might be something simple like that.