My Pi 2 sometimes does not power on properly -- just the red LED comes on and there is no further activity.
I've done this a bunch of times and there is a consistent pattern. If it happens with no HDMI cable attached, flicking the power (it's on a switched power bar) will restart properly, i.e., it will only happen once, then on the second try it's fine.
If it happens with an HDMI cable attached (the other end of which is to a display that is not on the power bar, and is on constantly -- and, as per comments below, that display has another, already active HDMI connection...), it will happen over and over (i.e., the pi will not power on properly). However, if I turn the power off, unplug the HDMI cable, then plug it back in, then turn the power on, it always restarts properly.1 I have been through this literally dozens of times in a row over the course of a few hours (turning off frequently in order to take the SD card in and out, for unrelated reasons).
This workaround with the HDMI cable is fine for me right now, but would be a real hassle under other circumstances (if this is a genuine issue, I'm guessing more people will show up here eventually asking about it).
The fact that this involves plugging and unplugging with no power implies something about a static build up to me -- but my understanding of electricity is pretty crude, and of the pi's circuitry, non-existent. I don't expect a solution here, but I am curious as to what the potential cause is.
1. I discovered this by trying with the HDMI unplugged, which also works -- but then plugging the cable in after boot causes a problem with the display resolution, so I tried this plug and unplug with no power and voila. Again, it is very consistent.