I just noticed that in my “Open with…” dialog box of Win98SE, there is a program at the top with no name (empty). Anyone of you had the same experience and managed to get rid of it?

Same here, I don't care about it. Nothing malicious.

Seems to open up an explorer window with C:\ if I try to use it to open a file.

That is exactly what I get, i.e., open up an explorer window with C:\ if I use it to open a file.

I managed to reproduce the same situation in another Win98SE PC with following scenario:
I created a text file and gave it an arbitrary name CRAZY.CRY, any name will do though, important is that the extension must be one that is not existent in the system. Then I copied Notepad.exe and gave it a name MyNotepad.exe, again here any name will also do. I right-click CRAZY.CRY, in the "Open With..." dialog box I click to tick "Always use this program to open this type of file", then click "Others..." -> point and select MyNotepad.exe. The system will create following key in the registry:

[HKCR\CRY_auto_file\shell\open\command] that contains in it (Default) C:\WINDOWS\MyNotepad.exe "%1"

When I then delete the content of the (Default) C:\WINDOWS\MyNotepad.exe "%1", i.e., the command key becomes empty, then the "Open With..." dialog box will contains the nameless (empty) program on its top line. To get rid of that nameless program, I simply delete the registry key above.

With the same way, I could get rid of the nameless program in another PC I mentioned earlier. In the registry I searched ALL command keys, trying to find the one with empty (Default). It happened to be [HKEY_CLASSES_ROOT\dMC.AudioCD.Autorun], I don't know what program may have left that key in my registry. With that key completely deleted, my "Open With..." dialog box has no more empty program.