Been searching everywhere and found this thread, it seems my DE10-Nano has the same issue. I've posted this in the fb group, but that thread will disappear in the fb scroll. I thought it best to also put it here for future reference.
In summary, tested on 3 different monitors, plus a tv, in various combinations with 4 sets of cables varies lengths (ranging from an aliexpress cheapo to expensive shielded av ones.) No hdmi video detected/displayed.
Board is new, stock configuration MSEL dipswitches setting. Tried with fresh Mister image, included angstrom sdcard, another card with lxde image from terasic website. Nothing.
Verified that it boots ok, ethernet over usb ok, putty in ok, webserver running ok. Just no hdmi on monitors.
Then tried with some HDMI converters I had :
DE10-Nano hdmi out > hdmi to av > av to hdmi > monitor.
And I get signal.. Awful quality, but now I'm seeing something on the monitor. I don't think there's such a thing as "weak" HDMI signal, it's digital, it's either there or not. So I don't even know what to think anymore.