lighting bolt and gear icon

One problem with this: my Power button does not work. The inner stem--the bit that the power button on the outer shell of the phone connects with--broke off, for some reason. What other options are there? Also, how do I fix the Power button?

I had a same "lightning bolt and settings icon" on my Nokia Lumia 625 today. Not able to come out of that screen. i followed all the above steps nothing worked out. I recently updated my phone to Windows 8.1. My phone was charged out and dead then i try to recharge it and end up in this issue. 

Looks like a serious issue and some one from WP (SW/HW) need to jump in and resolve it on priority. Just now the WP sales got little good progress. Issues like this will bring it down!!!! 

Thanks in advance.

So lets try this and see if it helps.

Hard Reset using buttons:

Press and hold the Camera + Volume Down + Power until the phone vibrates. Then release the Power key and keep pressing the Camera + Volume Down for a few seconds.

I did the power button ,vol down and cam button and it went to the low battery screen . I plugged it in and it restarted a minute or 2 later. My issue was caused by the battery running out of juice before it could shut down. I was playing angry birds star wars 2 on a low battery plugged in .it just drained the battery quicker then it could charge and when it shut down it went black then restarted with the gear and bolt. So the improper shut down is what I think causes it( or maybe a crash)