iMac G5 Unix Can't login

Hello.
I believe I have read somewhere once that there is a real and satisfactory solution to this problem. I use Mac OS 10.5.2, Unix. I have two User accounts and because I switch back and forth between them frequently, they both have Admin Priveleges.

No one else uses my computer. My computer is not connected to the internet, ever. (It is terrible in this country anyway)

Both accounts are password protected. Upon "boot up" or "logging out" to switch Users (I don't use the "fast-switch" option the system offers), I am presented with a window, requiring User Name, Password, and the choices of (not sure of order) Shut down, Sleep, Restart and Login.

No User names are present at that time.

Problem? I can't login. My password is rejected each time and I know it is right. Not only that, but the Login window, now has underneath the grey Apple Logo, the name of one of the accounts. This shouldn't be, unless it had been sleeping or in energy saving mode, meaning that particular account was still "active" if you will. But it wasn't.

What to do? I know the password is correct. Isn't there a way to get in that I don't know how to do but a techie could, or with some sort of Apple bypass software?

Before this, I just downloaded and installed a new version of VLC, Quicktime and tried iTunes 10.1.1 but that wouldn't take. Perhaps the fact I was still at iTunes, version 7, is why. But, everything else worked fine until I returned from the internet cafe (I don't have internet where I live), put in some new desktop pics from Pixdaus.com, turned the machine off and left for a few hours.
Came back, booted and can't get in!!!

Help please if anyone knows a way to safely log back in.
I haven't played with User accounts in System Preferences at all.
Thanks