Both monitors worked with HDMI, here are some specs to assist you: Intel(R) Core(TM) i7-6700 CPU @ 3.40GHZ 16 GB of RAM 64-bit operating system x64-based processor
you have an i7-6700 processor.
This is the latest driver for your intel graphics:
You should be able to download and install the exe version. This is assuming you do not have an add-on graphics card (like nvidia or amd). Do you know if you have nvidia or amd? If you do not have those, then install the Intel driver.
you can look in the device manager, or run dxdiag, or look at the back of your PC.
Or, you can download, run, and attach (using the paperclip) the results of this utility: