Please power off any many devices as possible, but leave the Mac that you normally use to administer the Time Capsule and the Time Capsule itself powered on.
On the Mac.....
Open System Preferences (gear icon on the dock)
Open Network
Click on WiFi on the left panel to highlight it
Click Advanced at the lower right of the window
Click the TCP/IP tab
Make sure that the setting for Configure IPv6 is set to Link Local Only
Click OK
Click Apply in the next window that appears
Now you should be back in the Network window again.....
Click on Ethernet to highlight it and then perform the same steps as above
Be sure to click OK and Apply
Restart the Mac
Open AirPort Utility to see if the AirPort router will now appear
If it does, then perform the same steps for WiFi and Ethernet on your other Mac
Then, unless your ISP has implemented IPv6 service and provided you with specific instructions to configure IPv6 on the AirPort router, you should change the setting for IPv6 to Link Local Only the AirPort router as well. Post back if you need more info.