Precision 7720 mini display port disabled

To my knowledge there's no way to disable the Mini DisplayPort output by design, so if it's not working, I don't think it could be a configuration issue.  If you haven't already tried toggling the "Graphics special mode" option, you may get different results by changing that setting, but the output is supposed to work either way, so that would just be some experimentation.  Otherwise, if you've already tried things like changing the cable and/or display (or you've validated that display and cable elsewhere), my guess is that this is a hardware issue that will require a motherboard replacement to resolve.