Try the other HDMI port.
The one near with power supply on the Pi, which isn't actually the one near the power supply on the Argon One case, at least in version 1. I had this problem myself, and it seems I am not the only one.
I had the same issue with the Pi4b in the Argon M.2 case. Use the other hdmi port and boot with TV on. MIne's been working flawlessly for weeks now.
I've used both HDMI ports on my Argon ONE M.2 Pi4B case without issue. The HDMI outputs are reversed from the Pi board. Looking from the back; output HDMI0 is far left, and HDMI1 is next to the USB-C power supply. HDMI0 supports up to 4K@60Hz (I'm using it) and HDMI1 only supports up to 4k@30Hz (I've proven it myself).
craigr
Well, mine works fine, but since I do SMD soldering professionally I'm going to check it anyway. One thing I don't like about this case is that inserting the board requires it to go into both micro HDMI inputs and the analog input all at once. This can't really ever line up completely, so it requires quite a bit of force to insert. Much more force than I would really like to use on HDMI micro connectors. I'm sure it could break solder joints.
craigr
When I changed to a 2.0 spec cable the plastic connector molding was a little larger. I use the Argon 1 case. The connector didn't feel right so I marked it out and filed the case so the connector fitted properly. It was a millimeter or two that needed filing so the connector clicked in properly. I guess it depends on your connector.
