Apple Remote Desktop doesn't work on outside connections

Question

I use Remote Desktop to control computers at another location from my computer at home (cable modem. This worked fine with my old (non Apple) router. I have upgraded to the dual band Airport Extreme and now Remote Desktop tells me that computers are offline (when they aren't)
How do I get Remote Desktop working? The Airport Extreme is not in double nat-mode.

Answer 1

Let's double-check your port mapping settings for ARD:
To setup port mapping on an DB 802.11n AirPort Extreme Base Station (AEBSn), either connect to the AEBSn's wireless network or temporarily connect directly, using an Ethernet cable, to one of the LAN port of the AEBSn, and then use the AirPort Utility, in Manual Setup, to make these settings:
1. Reserve a DHCP-provided IP address for the host device.
Internet > DHCP tab
o On the DHCP tab, click the "+" (Add) button to enter DHCP Reservations.
o Description: <enter the desired description of the host device>
o Reserve address by: MAC Address
o Click Continue.
o MAC Address: <enter the MAC (what Apple calls Ethernet ID if you are using wired or AirPort ID if wireless) hardware address of the host computer>
o IPv4 Address: <enter the desired IP address>
o Click Done.
2. Setup Port Mapping on the AEBSn.
Advanced > Port Mapping tab
o Click the "+" (Add) button
o Service: <choose the appropriate service from the Service pop-up menu>
o Public UDP Port(s): 3283
o Public TCP Port(s): 3283
o Private IP Address: <enter the IP address of the host server>
o Private UDP Port(s): 3283
o Private TCP Port(s): 3283
o Click "Continue"
o Click the "+" (Add) button
o Service: <choose the appropriate service from the Service pop-up menu>
o Public UDP Port(s):
o Public TCP Port(s): 5900
o Private IP Address: <enter the IP address of the host server>
o Private UDP Port(s):
o Private TCP Port(s): 5900
o Click "Continue"
o Click the "+" (Add) button
o Service: <choose the appropriate service from the Service pop-up menu>
o Public UDP Port(s):
o Public TCP Port(s): 5988
o Private IP Address: <enter the IP address of the host server>
o Private UDP Port(s):
o Private TCP Port(s): 5988
o Click "Continue"
(ref: "Well Known" TCP and UDP ports used by Apple software products)