What is the MAKE & MODELS of both Monitors and what resolution are you running each one?
If you go to Windows Settings - Display does it show both Monitors connected and at what Resolutions?
On the HDMI Monitor have you tried changing the Resolutions through Windows Settings - Display to see if you get any video?
In Device Manager under Monitors, does it show both monitors working correctly? Do you have the Monitors Drivers installed from the Manufacturers?
On the HDMI Monitor, Do you have the Monitor set for HDMI?
I don't believe this is a driver issue but do you have the latest R9 270X Driver installed from here: AMD Radeon™ R9 270X Drivers & Support | AMD