Not sure how to get the link back, I'll post later tonight if I find the code that enables that. For the time being, you should be able to access your admin panel through the following link:
http://www.yourdomain.com/admin/index.php
And your register link should look like this (with an sid= value at the end, but ultimately this works too)
http://www.yourdomain.com/profile.php?mode=register
If you get a blank page on that, then you've got something in the coding for profile.php that's not right, and most likely because of a mod or something that you were implementing on it. Try reversing what you changed (if you know what you changed, lol) or scanning the code for missing closures etc. You'd most likely get a syntax error on access if you were missing a character.