I had to pay Nikon Melville $251 including return shipping to fix the 10 pin connector on my D800e. I would guess that the HDMI repair would be about the same.
Note that's it likely the Nikon authorized repair centers are not yet authorized to repair a D800. This was the case for what I considered a simple warranty repair on my D4 earlier this year.
Gary in SE Michigan, USA. Nikonians membership - My most important photographic investment, after the camera. D4, D810, D300 (720nm IR conversion), D90, F6, FM3a (black), FM2n (chrome) YashicaMat 124, Graflex Speed Graphic 4x5 My Nikonians Gallery & Our Chapter Gallery