First suggestion is to get another power supply. Sounds like despite how it is marked or it cannot handle the current surge. Some power supplies have a slow start and do not like a lot of current until after a short period of time. I have actual seen these types of supplies myself.
Gerald
If I can just chime in, I also get this behaviour quite often when using a usb cable plugged into a (min 1A) wall wart. The LED will switch on for a few hundred milliseconds and then switch off, rinse and repeat.
To solve it I unplug, and plug back in a few times and it tends to get going after a few tries.
Cheers,
Jack.
Gerald,
No I do not. A lot depends on what else may be plugged into the system, what SD card you are using, some take more current than others. I know it isn’t much as it boots over USB, which limits to 500mA and 100mA initially… The inrush current for DC is no different than USB as they connect to the same rail on the PMIC.I used a wall wart before that showed the same issue as it was designed for a specific piece of equipment. I can’t recall what it was for, but I know they are floating around at a lot of surplus stores.
Gerald
Not sure what caused the damage, but based on your description, damage has been done. I suggest you submit an RMA request and get the board looked at. http://beagleboard.org/support/rma
Gerald
Yep, I just saw it come through!
Gerald
I had a similar problem with mine. I found several warts in my box that
measured 5.2 volts regulated but no 5.0 volt ones. So I tried a 5.2
volt unit. No go. The power light lit but nothing else happened.
My solution was to take a 9 volt wart and put an LM7805 regulator and a
couple of 1uF film caps in the cord. with a little heat shrink over it,
it doesn't look much different than one of those EMI chokes. 5.0 volts
worked perfectly.
Probably would be a good idea to print on the box insert how tight the 5
volt requirement is. Also on the website, recommend some
Digikey/Mouser/Newark part numbers of known good warts. I'd have gladly
spent the extra money for a known good wart.
Frank, as for plugging in a 9 or 12 or whatever volt wart, well, you're
on your own there. The jack is plainly labeled for 5 volts.
John
Yeah a good power supply is required for the BeagleBone else you will likely smell the magic ozone smoke if you attempt using something with more than 5V output.
Actually, there is a protection circuit that should shut it down to prevent damage, depending on the ramp time of the power supply when you turn it on. If it is really fast, it can sometimes get through…
Gerald
Maybe it would help if the BeagleBone had a LiPo charging circuit and two or three 2-pin JST-PH connectors! 
Maybe. Then again if we added everything people thought would be helpful, no one would buy it. Then again, you can build a cape and use the integrated battery charger on the PMIC to add this feature.
Gerald
Really? I thought I had remembered seeing a couple of threads about the PMIC not having enough current to simultaneously charge and run the BeagleBone at the same time? Are there any hardware reference designs that integrate the PMIC, that could facilitate two or three JST-PH connectors to charge and maintain a couple of LiPo battery packs such as those sold by Adafruit? With some initial tests I can get about 8 hours of life from a BeagleBone A6 running on a 10000mAh battery pack I have here; having the batteries connected to a cape with PMIC capability would make for an awesome mobile platform, especially if there is new power management capabilities in the 3.8 kernel that Robert Nelson et al have been working on.
Goodness no. It can handle 2A current and the board only takes, depending on what is on the USB host, about 1 amp. If you look at he datasheet for the PMIC it gives examples and describes the operation of the charge circuitry. USB power is limited to 500ma by a PC, but if you can get more, you can set the PMIC to let more current flow for the board and the battery. There is a header on the board that provides access to all the signals needed for a battery cape.
Gerald
Realistically, the highest charge rate the PMIC can do is 700 mA and the
longest timeout you can set is 8 hours, so batteries larger than 5 Ah
or so really aren't reasonable. But I get about 2 hours on a 1 Ah
lithium battery at idle on my bones at room temp with no capes and no
power management code.
The lacking part of the equation is there is no gas gauging ability in
the TPS65217. So you'll need some external way to determine how much
battery life you have left if you plan to run for extended periods of
time.
-Andrew