Usually, if you can't play the MIDI files direct from the database, you can at least download them by right-clicking on the "click to play" link and choosing to download. then you should be able to double-click on the MIDI and play it, unless your computer is really messed up. Windows comes with a MIDI player, and I think the Mac operating system does, too.
Click here to download the latest version of Windows Media Player. If you install it, it will usually overwrite all the goofed-up software you have and make things work properly.
-Joe Offer-