Time Capsule backup works on one, but not all computers.

We have a Macbook and an iMac, both on Snow Leopard. Set them up on TC for backup several months ago, and they worked for a while. Then it stopped working for no obvious reason, with the message:

The network backup disk could not be accessed because there was a problem with the network username or password. Open Time Machine preferences to select the network backup disck and re-enter the correct username and password.

Of course userame and password were correct, because, first of all, they had not been changed, and second, because I could put in the wrong pw and it immediately would reject it. As it is, it takes it, counts down for 120 seconds, and then gives the above message.

Bought a new Macbook Pro, using Lion, and it works with the TC, seemingly proving that all settings on the TC are still good. Tried resetting TC. Tried the Cmd-Alt-p-r reboot, but neither worked.