Noting that Godaddy offers two hosting options, linux and windows, which would most likely work best with your site? I had Linux, switched to Windows to see if it'd work better... But I don't think it does. Seems like I have less permissions on Windows, so I switched back.

What is your php version? I run my site on php 5.3 and the login system works just fine. If your PHP version is lower than that, you could ask your host to update your php version? ^^

Also, it seems that your .htaccess is not functioning correctly, hence the odd behavior with your URL? Does your host support mod_rewrite, and if so, it is enabled? This could be the cause of the url's odd behavior.

Actually it does work on both Linux and Windows, I think your problem has something to do with godaddy's PHP configuration. Is the login/password problem the only issue you have? Do you happen to encounter any other issues?

Login, registration, and password reset all pretend like nothing is happening.

mod_write is enabled, according to GoDaddy. Also my PHP is 5.3, as yours is. Not sure what the issue is. Able to connect FTP and the install seems to go through. One interesting thing is when it creates the first UN, it doesn't seem to accept the password I give it. It seems to generate a random, long string of characters. Even entering that string in does not grant me access and changing it does nothing as well.

If you are seeing that long string in the database, it's normal, since it prevents the admins from seeing other people's password. The password is enconded.
Creating a new user and giving it admin privileges doesn't work? Because for me the first Admin could never login or reset the password also

IntoRain is right, the password is encoded in database so you are not supposed to log in with that password anyway. Did u say that you can't even register on your site as a non-admin user?

Correct. When I try to register, it acts as if nothing happened. And no. I've tried creating up to three different logins and none of them can access the site or the ACP.

I see, thats what makes the problem strange, something that never happened before with Mys v1.3.3 and v1.3.4. To think that your site runs flawlessly on x10hosting, I doubt it has something to do with GoDaddy's PHP configuration. If only I am able to actually log into your FTP and run some test code to figure out what exactly is going wrong.

Well, the option is still available for you to log into my control panel at GoDaddy.com. ^.^ I'd sent you the un and pw for my main acount.