I just installed DarNified UI after doing a clean Oblivion install, and I've been greeted with this:
http://img820.imageshack.us/img820/5919/oblivion201101030809082.png
I can't click anything in menus as well.

What's going on here and how do I fix it?

I *think* there is a modified leveling screen menu included in DarN, not entirely sure though. Maybe need to verify that in the readme. Say overwrite Yes if so prompted.

Did you install DarN with the OBMM?

I'm surprised you get this funky screen. I installed DarN (with OBMM) also during an ongoing character and it shows up everything correctly.

Have you changed your INI to include the new fonts? And have you installed them?

Oops... I figured they would be in the ini from last time it was installed, but I forgot that it was a new ini...

Yeah, change your fonts in the Oblvion.ini file.

That's your problem then (seen it myself when rebuilding a 'damaged' ini.)
Add the new fonts to the ini, or reinstall DarN so that it will do so automatically (that is what I did.)