If you are able to open the site live, then the extensions are operating.
If you aren't familiar with this process, I will give you the way I normally go about it.
1. Create a blank folder in MyDocuments\MyWebs or wherever the FP webs are stored. Do not create a web, just an empty folder, e.g. if the original web was apples, then apples2
2. Now open FrontPage. Go to File >> Open and type the site URL in the textbox normally reserved for page names. Depending on your connection speed, this could take a while.
3. Open any page.
4. Go to File >> Publish Web". Use browse to locate the empty folder. If FP says it needs to create folders, let it do it's job.
Before we go any further, it looks like the previous user was utilizing one of the addins available form
FrontLook Haven't used them myself, so couldn't really say which product.
If you continue having difficulty, it may be necessary to locate the files associated with this and delete them. The unfortunate thing is that it may have been used for a fundamental part of the site e.g. effects for one.
Once you have the web published down to the PC. Open the new folder in FrontPage. You should then be able to make changes and publish back to the server.
Wont bet my life on this, but this is the route I would take. If the site doesn't open live, then the extensions may need to be reset or uninstalled and reinstalled. If the extensions are operating properly then there could be a problem with permissions at the server level.
A general note: The web may be utilizing component pages which rely directly on the extensions e.g. FP forms for one. This would not only require the extensions, but also using the built in Publish Web function to http location. Use of FTP can corrupt then necessitating a reinstall or reset.
Additionally, Hover Buttons would be relying on the _fpclass folder and the _borders folder would contain any shared borders in use or stored for later use.
Hope I have been of some help,
Micheal Smith
FrontPage Form Tutorials & Form Script Examples