I have never heard of or seen a "power down button". Unplugging the TV and holding the power button for a minute or so sometimes will do a hard reset on the TV, is that what you seen?.
On your problem, chances are there was a spike that came down the power line when your power went out and it took out at a minimum the main fuse in the TV, you can remove the back and replace that fuse on the power board and see if it comes on or blows the fuse again, if it blows then look for a bad rectifier or shorted FET transistor in the hot section.
Check the remote control for its infrared emission. Check it with fresh batteries. Check it by pressing all the keys. You can detect the presence of infra-red emission from the remote control, using a cell-phone camera. If you wish to get more details about how to check a remote control, please visit this site. One among the posts has details about it. Surf the site with patience. http://remotesearch.blogspot.com/
Search the site by type in this key phrase "how to test a remote control "in the "search box at the top right of the display window of the Homepage" to get the related post quickly. https://www.youtube.com/watch?v=F8oYoZslgbs
Fault with the main power supply regulator board. Check and replace damaged component/s at its main power regulator [SMPS] section circuit.Contact any service technician.If you wish to get some details; check the site linked here.Surf the site with patience.Pull up older posts. http://electronicshelponline.blogspot.com/ It will be best to replace the power supply regulator board as card basis.
Hi, First check that you have good power coming in from plug. If that is good check out power board (capacitors Bad) replace if oozing out or bulging out. If you are good with soldering then do so.
Replace with same capacitors or better ones.