As far as I know, the National Desk inside the Dolphin Hotel is still open. Here are the hours of operation as listed on National's web site:
Orlando -Walt Disney Dolphin Resort
ORLR13
1500 Epcot Resort Blvd
Orlando, FL 32830
US
Tel: (407)934-4930
Fax: (407)934-4366
Hours of operation:
Sun-Sat:08:15 AM-03:45 PM
Service(s) available:
CN-Counter
MG-Meet And Greet
You cannot drop off cars at the Dolphin location. You will be directed to the Car Care Center (near the MK) to do that. If you drop your car at the CCC, National has a complimentary shuttle that will take you back to your resort. Some people report that the shuttle will take you to one of the parks if you'd rather do that. Be sure to double check the CCC hours before you drop off your car if you need the shuttle ride. CCC is not a 24 hour location. Here is what National's web site currently says about the CCC:
Orlando- Walt Disney Car Care Cntr.
ORLR02
Lake Buena Vista, FL 32832
US
Tel: (407)824-3470
Fax: (407)824-8230
Hours of operation:
Sun:08:00 AM-06:00 PM
Mon-Fri:07:00 AM-06:00 PM
Sat:08:00 AM-06:00 PM
Service(s) available:
CN-Counter
MG-Meet And Greet
You cannot actually pick up a car at the Dolphin location either. You can do the paperwork there, however. To actually get your car, you will be taken (sometimes after a wait) to the Car Care Center via National's complimentary shuttle. There is no EA or EC service available at either the Dolphin or the CCC.
IMHO, you are better off to just do everything at the CCC. You can call for the CCC shuttle to pick you up at your WDW resort if you need a ride over there.
HTH.