Thanks for the additional details.
Since the DVI connection on the dock is working fine, it’s likely the case that the DisplayLink driver has installed and is functioning properly (otherwise, both displays would not work). If you have one available, the first steps we’ll want to take are to swap out the HDMI cable with a known-good cable to rule it out as a potential culprit.
If this isn’t an option, you could also try connecting the HDMI cable directly to the HDMI port on your laptop and seeing if it displays without issue.
Thanks for your patience while we work to help!