Modules not showing up in the Extension>Modules

[Stockhlam]

Hello!
I'm using CMSMS v1.4.1 and have a problem with modules: when I go to Extensions>Modules:
1) it shows only some of the installed modules; I had more than 10 modules in the list, but now it finds only 6 modules, and sometimes even 5:
  Album
  CMSMailer
  Comments (this is not installed)
  DLComments (this is not installed)
  DLSupport
  FCKEditorX (this tend to disappear sometimes, I don't know why, seems to be random)
2) I can't add any new modules; file names and directory structure is absolutely correct but cmsms just doesn't show them. Though I can add and remove any of the previously listed modules as many times as I wish.

Before the problem appeared I was editing only content, at least I can't remember changing any 'system' data. I haven't modified any .php files.
MySQLAdministrator showed an error near one of the cms_module_search_XXX tables "Incorrect information in file 'blablabla .frm'". Today I deleted all cms_module_search_XXXX tables and the "Search" row from cms_modules (kind of uninstalled it). But that didn't help either.

I installed a fresh CMSMS in different directory and with other table prefix and everything worked fine, it even finds incomplete modules. So there has to be something wrong with the database or files.

Is there any way I can fix this? If there isn't,maybe you can suggest an easy way to export only content (pages, stylesheets, templates, menus) and move to a clean CMSMS?