You will need to check what version of HDMI your monitor supports. That will tell you what the maximum resolution and refresh rate it supports. My old 120Hz monitor had HDMI and DVI ports only as well, however, only the DVI port on the monitor could support 1080p @ 120Hz and the HDMI could only support it @ 60Hz. You may need to look into getting a DisplayPort to DVI adaptor. Make sure it is DVI-D (Dual Link) as I believe that is the higher bandwidth.
