I've run across the same problem as discussed in thread
http://groups.google.com/group/firebug/browse_thread/thread/00b6a5300....
I'm on Windows XP with Firefox 2.0.0.6 and Firebug 1.05:
"Unable to show styles. You must install DOM Inspector.". Of cause,
DOM Inspector has been installed, but - as others have reported - my
Firefox installation is an old one, with the initial install being
Firefox 1.5, and upgraded ever since.

Didn't want to reinstall, so I did a diff with another (newer, clean
2.0) Firefox installation, and removed the following files in
"%ProgramFiles%\Mozilla Firefox", as they seem to be remnants of the
initial Firefox 1.5, and now part of 2.0:

components.ini
defaults.ini
chrome\inspector.jar
chrome\pipnss.jar
components\inspector.dll
components\inspector.xpt
components\inspector-cmdline.js
defaults\pref\inspector.js
extensions\Extensions.rdf
extensions\installed-extensions-processed.txt
res\platform-forms.css
res\builtin\platformHTMLBindings.xml
res\inspector\search-registry.rdf
res\inspector\viewer-registry.rdf

Detailed steps:
1. Uninstall Firebug.
2. Close Firefox.
3. Remove above files.
4. Start Firefox.
5. Reinstall Firebug.
Bingo! Firebug now shows styles.

I hope this helps someone; if that doesn't work, you can still
completely uninstall Firefox and wipe the directory, as suggested by
others.

-- Ingo Karkat, 01-Aug-2007