After staying up half the night, the problem got solved by finding a bug, and I thought it might to good to post the result here for any Mac users with Airport like myself.

-Use HEX password (this can be found in Mac Airport Utilities menu bar) and set WEP to 40 (64) bits.
-Enter primary and secondary DNS
-Check "Auto retrieve IP adddress"

The bug I came across was this:
-The SSID will automatically be a copy of the Network Name. CHANGE the SSID to something else;
-Fill in the abovementioned info;
-Save and close;
-Now try to connect
-Interestingly, instead of the 100th time 'connection problem' being shown you will receive a dialog window with the SSID NAME CHANGED BACK to the Network name (as it was originally) and with a request to enter your WEP password. You have already done it, but enter it again (don't forget tp choose 40 HEX first).

For some bizarre reason, the connection will now work perfectly.
By the way, I am running OX Tiger and the 770 is the latest software version December 2005.
Good luck!
Tadeyev