Is your adapter an active HDMI(PC)>DP(monitor) cable? An HDMI output cannot translate properly to a DisplayPort input if you use a passive adapter. And, importantly, these video cables typically work only in one direction so you can't just turn them end-for-end and expect them to work. Are you sure you used the HDMI-Out on the PC, not HDMI-In? BTW: The maximum resolution supported by the PC's HDMI port is 1920 x 1080 at 60 Hz (24-bit).  Have you opened the monitor's own On-Screen-Display (OSD) to make sure it's set to use DP as its input port? If it's set to "Auto-Detect" try changing the OSD setting to DP. And, the USB-c port on this PC doesn't carry video or audio, so that's not going to work, even though it works with your lappy.... Read this too...
My friend gave me a Dell monitor (E2420H) and it has a displayport and VGA.  MFG June '21 I cannot use it as a 2nd monitor.  Tried HDMI out to displayport and no detection.  Tried the USB-C to displayport with no detection (my Samsung laptop's USB-C port does work with the monitor).  Is the only option using the VGA port? 
2nd Monitor Connection