The only way to test if the issue is being cause by the keyboard will be by testing another one.
There is a BETA Bios version that you can try. This Beta BIOS is to check a potential fix for problems entering BIOS Setup with certain monitors and TVs. It enables 1776x100 when 1080i is selected and add 1184x666 when 720p is selected for HDTV via HDMI.
Please report back whether or not this BIOS allows you to access BIOS Setup with F2.
https://downloadcenter.intel.com/Detail_Desc.aspx?agr=Y&DwnldID=24079
