I guess a couple of observations.
Some TVs have specific HDMI inputs or even DVI inputs for computers. I don't suppose you have seen anything that mentions that in the literature?
Also, not all HDMI cables are alike, an early version might limit the resolution in some manner. The fact the TV stops showing the signal after boot would make me think when the system went to its normal resolution the TV could not see it.
Most TVs are also 60 Hz refresh rate as is an LCD type monitor. A VGA monitor might use something higher. If you had the TV shown on your Desktop options, you could check that.
Video outputs may also be limited as to which ones you can use at the same time. Do you have anything other than the HDMI and VGA outputs?