I haven't seen this posting again until today when I got an email notice. Anyway, there are two problems here and maybe they both have the same answer, but let's try to get things straight and figure that out.
rynbow,
You say that you couldn't get the airport connection to work until you turned the password off. I take that to mean that you left the password field blank and you can connect to the internet. Most, maybe all, wireless routers come defaulted with no WPA or other security so the password for access is none. If it is working with no password that makes your life easier. Stay with it.
Henri,
I guess, if I'm reading your input correctly that you have one Mac with three users and a router. You mentioned the airport signal indicator so that means you have a wireless router and you are accessing it through the WiFi port. If you set up your router initially with security enabled by going through the set up in your browser talking to a device called 192.168.0.1 (an ip address) then you must have all the info that you gave your router for the security. If you changed the user account from administrator to something else and you changed the password from blank to something else, then both of those must be used to gain entry back into the router. I have never set up a router for security but I would imagine that the password that you gave out to each user of the router is unique and not necessarily the same as the admin password for the router. If on your Mac you are connecting to the network and it is asking you for a password and it is not taking it, then you may have to totally reset your router and put in the passwords again.
Also, the "signal being zero" comment you made still wasn't explained, but I am assuming that you are referring to the icon in your menu that is shaped like a big piece of pie and it has no lines showing in it. If this is the case, you are either in a very low signal level spot or your airport is turned off. Regardless, your password is not getting through to the router and it won't do anything except its job to keep you out. Click on the airport icon in the menu and make sure that your airport is on. If it is, then pull it down to the network connection section and scan for signals. If your airport was never configured you should see it with a name default. Otherwise, it will have whatever name you gave it. Tell airport you want to use whichever signal you are seeing and wish to connect to. If you are asked for a password, put in what you think is your password. If that is rejected, then let me know and I'll explain how to reset your router, which is a big pain to do, but easy to explain. Important: make sure you are connecting to your router. There very well may be several other signals in there from outside sources like WiMax and other people's home routers.
For both Henri and rynbow,
Please ask me more questions if none of this makes sense or if part of it does but things are still not working.
Steve