Solution 1:

Notorious problem I'm afraid. Not so much missing software but you'll have a version of DirectX so advanced it's incompatible with early games. Some users have had luck running Diablo using Compatability Modes for Windows XP or earlier, or even Virtual Machines/DosBOX or equivalent, so you could try those first?

Solution 2:

This may sound weird (and I have actually done this to play Diablo on my Win 7 laptop), but right click on your desktop and click on Screen Resolution. Leave that open and then run Diablo.