The power light flashes are error codes. I couldn't find an official Apple support article about them but I did find this. AS I recall from the time I had it happen to me, these are correct.
short, short, short – The display is detecting either a wrong video format, or an unsupported resolution. Verify that your equipment is compatible, and then restart the computer. If the issue continues, reset the PRAM. If you have reset the PRAM and are still getting the error, shut down the computer, power cycle the Cinema Display, then turn the computer back on.
short, long, short – Make sure you are using the correct power adapter with the display. This alert will only appear on displays built in 2004 or later, which require an external power adapter.
short, short, long – The display is detecting a backlight error. Check your display’s power connections and restart the computer. If the problem continues, contact Apple or an Apple Authorized Service Provider.