I have a Mac Pro early 2008. I'm sending this message on my iPhone 4S. Comcast cable had an outage during a storm in our area. I was using my Mac Pro when service went to the dogs. After several false starts, Comcast finally came back. Two other Macs in our house were back in business but my Mac Pro showed a flashing white light above the On/Off button instead of the normal steady light. I am able to shut the off the flashing light by holding the button down for a few seconds. This morning, the situation has not changed. I do have an external backup drive that backs up at least every hour. I'm not worried about data loss, but I am very interested in how to get the Mac Pro back in service.

The first step is to reset SMC. If that doesn't resolve it, you'll probably have to bring it in for service. I don't know if replacing the internal battery is indicated, but it's worth considering.

Jon:
Thanks for the reply. I followed your suggestions by going to the Apple help page (not the open forum). The more I thought about it, the more I think something will have to be replaced--either a battery or a switch or both. I'm scheduling an appointment at the Genius Bar ASAP. Your suggestions were very helpful. Thanks.

The symptoms described might point to POST signaling, which can manifest as Power light blinking. If true, the number of blinks in the repeating series indicates the underlying issue, which may still require a visit to the Genius Bar.

I just got back from the Apple Store. After a LOT of diagnosis, they traced the problem to failed RAM. They removed the RAM and the problem disappeared. I'm writing this post on the rejuvenated Mac Pro. What a relief! Thanks for helping me decide I needed to go to the Apple Store. It really did require their diagnostic capability. I was resisting going because the Mac Pro is such a heavy beast to haul from the parking place to the store. <grin> Apple folks kindly helped me move it from the parking lot to the store and back to the car. I call that super service.

alternaut: Thanks for the suggestions. They further convinced me that going to the Apple Store was the right move. The blinking lights had no pattern the were rapid and consistent. I may not have made that clear earlier.

there was a pattern, it was just too short of a pattern to be recognized as such... one blink! (and it repeats the pattern indefinitely)
So where three blinks is blink-blink-blink.....blink-blink-blink.....blink-blink-blink.....
one blink looks more like
blink...blink...blink...blink...blink...
and is less obvious as a "repeating pattern of 1's"

FYI, according to Apple Kknowledge Base HT201702 Bad or missing RAM should cause the power light to continually blink once per second.

As usual, the experts here nailed this diagnosis. I found out for sure by taking it to the Apple Store for diagnosis and treatment. All is now well except my early 2008 Mac Pro is getting long in the tooth. It can't do some things provided by Yosemite, but those things aren't really a necessity for my operation anyway. I am, however, starting to look to the future. I now have 6 GB of RAM instead of 8. Frankly, I don't notice much of a difference.

Thanks again.