I just had the same issue yesterday. This will sound wacky, but here is what solved my issue.
We recently implemented deploying printers with group policy. In Windows 7, it is important to keep all printer drivers up-to-date for word to start successfully because when Word starts, it calls the printers.
As a test, try removing all the printers from one of the issue machines, and see if Word starts working again. If it does, you have the same issue we had! :-)
Best of luck,
Kody Burg