The Outlook Express desktop client stored emails as .dbx files. At least the client distributions that came with Windows XP.
Try switching to a specific disk (
C: in the example below), then searching a disk for files with the .dbx files via the Command Prompt (i.e. cmd) as such:
dir /s *.dbx
C: in the Command Prompt, then pressing Return, you switch focus to the C: disk (i.e. C: drive). Typing
dir /s *.dbx, then pressing Return, will cause the computer to output all the locations of files (emails) with the .dbx file extension in the Command Prompt.
There are still three additional pieces of information I will properly incorporate into the answer at a later date:
Instead of outputting all locations of .dbx files directly into the Command Prompt, you can write (save) them to a file. To do this you replace the second line of code (above) with:
dir /s *.dbx >> dbx_file_locations.txt
Where dbx_file_locations.txt is the name of the output file.
It may be that the "disappeared emails" are no longer in .dbx format, in which case they may be in either .bak format, or some other compressed format (e.g. .rar). In such a case, the above solution would need to be followed by:
dir /s *.bak
There are some GUI tools built specifically to trawl through all user-selected desktop drives/disks for .bak and .dbx files. Will add links to these later.