What version of OS X are you running? And is this the retail version of Office v.X? Also, how did you install Office X? Did you use the installer application or just drag and drop the applications you wanted to your HD (which is the method I would recommend... screw installers if you don't need them : )
You might want to boot the computer into single user mode (startup computer holding down Command-S ) and type "fsck -y" at the command prompt. If it finds any errors and it says your file system has been modified, continue running fsck -y until it doesn't report any errors anymore. At this point, type "reboot" and see if you're able to launch any Office apps.