One thing you could try:
Make a backup of 'C:\Windows\System32\inetsrv\config\administration.config'.
find the line
<add name="Impersonation" type="Microsoft.Web...
and make a copy of it just below, then replace 'ImpersonationModuleProvider' with 'FormsAuthenticationModuleProvider' in the new line.
further down in the file in the section:
check whether there is an entry:
<add name="FormsAuthentication" />
and if not, add it.
I don't know whether this will fix your problem or why these entries are missing in the first place. But it is worth a try.
Otherwise I would re-install IIS.