The cable being high speed is not an issue.
Check that you have the HDMI connection on in the video or graphics control panel. If your monitor is higher video resolution than the TV then you will need to set the TV to it's native resolution (probably 1920x1080).
The order you boot the PC and select that HDMI input on the TV makes a difference. Try booting the PC after you select the input on the TV. The cable itself can be an issue especially if it's longer than 2-3m. Try a different cable. Try a different input on the TV.