I haven't had direct experience debugging HDMI issues, but I suggest trying some of the config.txt options listed at:
http://elinux.org/RPi_config.txt#Video_ ... figuration
First, try setting "hdmi_force_hotplug=1". This might tell RasPi the monitor is always connected.
If that doesn't work, try "hdmi_safe=1". It will probably set the wrong resolution, but it gives you a starting point. If "hdmi_safe=1" works, try the equivalent "hdmi_force_hotplug=1, config_hdmi_boost=4, hdmi_group=1, hdmi_mode=1, disable_overscan=0". It should have the same behavior as "hdmi_safe=1". Then remove the options one by one and see when it starts to fail.
Another thing that might work is to use the "tvservice" command to find out what your normal monitor setting is:
http://elinux.org/RPi_config.txt#Which_ ... monitor.3F
Then put those settings into config.txt, along with "hdmi_force_hotplug=1".
Hope this helps.