RichAllen: I want my $5.99 back!
Oh come on, you haven't even tried to get it running yet. There are quite a number of reasons why a game may not run and you haven't given us any details of what you've tried to do, nor what your system specifications are.
So firstly, contact GOG support if you haven't already done so.
Secondly, what are your system specifications?
Then onto the usual fixes:
1) Have you tried running as admin (even if your account is an administrator account)?
2) Tried different compatibility modes and disabling visual themes via the game shortcut?
3) Where is the game installed to? If it is Program Files (x86) then uninstall and re-install to an unprotected folder such as C:\Games\...
4) Being a DOS game it uses DOSBox. So try using different graphical settings such as Overlay, Surface, DDraw, etc (should be available in the GOG setup shortcut for the game).
Although number 4 may well be the solution here I still recommend the previous ones as modern Windows OSes (Vista onwards, especially 64-bit) are a pain with old applications and games when installed into Program Files unless you disable all the built in security like UAC and DEP.