Outlook Personal Folders

From the "View" drop down, select Personal Folders.

I can see the folders fine, except under Personal Folders, all the folders disappeared excepted the folder called Deleted Items. Choosing View doesn't help.

It sounds like you have more then one .pst file and you currently have the wrong one.
First do a search for ".pst" files on both the hard drive any drives on the network.
Next add the addition personal folders (.pst) to your Outlook. You can go back and remove the one(s) that aren't needed.

I don't understand when you say you can see them fine but also say they disappeared?

Goto Tools,Options,Others,AutoArchive:
See "Default archive file:"
If the pst file still there this is your default pst file on your outlook. If you have exported some other pst files like personal folders then try to search all your pst if you have found some of it try to move the pst files you should not be able to because you haven't closed it from outlook. Try to copy a pst file and rename it open
it on outlook see if your personal folder will be there. Lastly you can always used Tools, Find or Advance Find see where your personal folder go.
Hope this helps.