I haven't used Outlook Express in ages, but I assume that if it is possible to import those emails, it would be through some "import" option and not by just double-clicking the old exe file. Actually, doing that should not even work, and so I assume that what is happening is that the shortcut you created has the directory address that matches the installation of OE on the new harddrive - since that is now your C drive.
There might be a some kind of a profile file saved in your old harddrive that has all that information. Somehow getting that file into the new harddrive would be the solution. I use MS Outlook and that's how it works there - not totally sure with OE.
Also, what OS are you running? That could help in finding the folder where the information is stored. And what OS were you running on your old HD?