How did you install? Migration or installing from installer?
What kind of fonts? T1, TTF or OTF?
In Windows Explorer search for adobefnt*.lst and delete any found files that have a two-digit number in place of the asterisk. LEAVE THE OTHERS.
I cannot find a adobefnt*.lst.
Where should it be? In the Adobe InDesign folder? Or?
I installed all my fonts in the windows font folder. Before the new install (my HD crashed) of CS4 I had no problem with selecting any of the fonts.
There are typically many of them scattered around in the Program Files directories and in your user profile. Use the Search in Windows Explorer to find them.