My suspicion is power supply and grounding. The presence/absence of HDMI cable may help or hinder the power supply by the addition of an alternative ground path.
I'd quite like to simplify this.
Remove all USB devices. Connect ethernet. Use an sdcard with a clean install an no config.txt changes.
Boot up. ssh in (even if you don't have a display the IP address is likely to be the same as previous boot).
Report output of:
Code:
tvservice -s
tvservice -m CEA
tvservice -m DMT
tvservice -d edid.dat
vcgencmd version
vcgencmd get_config int