It is possible that your DirectX installation was somehow corrupted, or that your installation is set up in such a way that Grim Fandango cannot detect that you have it installed.
To be sure that it isn't a matter of you not having it installed properly, go and download the latest version of DirectX from here
. Install it, reboot, try Grim Fandango.
If it still fails, then clearly the game is not managing to detect your installation of DirectX after all, despite it being there. In this case, try using an alternate launcher such as this
one. It's a long shot, but Benny's launcher may
skip the DirectX checking procedure.
If none of that helps, then I'm really not sure of what to suggest. Outdated graphics card drivers could potentially be a culprit, so make sure that you visit your card's homepage (nvidia.com for example, if you have a Geforce card) and grab the latest set.