An -almost- similar problem here. It happened like 1 times out of 5, that the Box showed it's lights as if tuned on, but gives no signal to the TV. Than I have figured this one out: if I turn on the Box first and the TV right away, than it would stuck to boot, but if I wait like 10 secs after tuning on the Box to power on the TV, it will -most predictably and regarding my observation based presumptions so far- boot up just fine.
I don't know how the powering on the TV can be affect the Box :

, but it just seams this way...