I'm assuming you're trying to set the password for a user, not the system password? If this is true, and if the default account on the system is an administrator account (which it likely is) With no password, you can always make a new basic user account with a password, then make sure you have a second administrator account with a password for times when your normal primary user account just isn't useful. Or (still assuming the account has no password set currently), you could assign a password to the current account. After that, you could maybe delete the original password-less account from the system. All of this can be done through System Preferences --> Accounts (or Users, or something to that effect. It's been a while since I used 10.5.8).
But if the current user account has a password and you don't know it, you'll have to wait...
Once you get the 10.6 installation disk, you can wipe the hard drive yourself and start from scratch, making a password-protected admin account during initial setup. Then you can make a normal user account for regular usage.
However, if there is a password on the system preventing its boot, Apple can probably offer advice. Google might actually offer better advice. [Seriously, I know articles about such a problem exist, and you can find countless threads on the topic around the Internet with decent solutions].