If you don't have an HDMI port on the front of the TV, you're out of luck in your current configuration.
I find it nearly impossible to believe that there's no way to access the back of the TV without destroying cabinetry. Assuming you have an HDMI port on the back, you could connect some sort of an extension cable from there to a more convenient location. There are various wall plates available with HDMI and other ports; something like
this one might fill the need well (and let you hook up an old-school Nintendo or whatever as well).