I got new speakers a few days ago. I briefly listened to them when they arrived. "Break in" 5 days in a storage room, within break-in period, power outage happened - when I came home, I noticed my clock was blinking "12:00", speakers were still playing. Yesterday I listened to them, something just didn't sound right. Because they are new to me, I am not sure whether they are new sound to my ears, or power outage caused some kind of speaker-breaking-sound-spike? How can I find out for sure?

You'll have to be a little more specific on what "doesn't sound right" means.

It is certainly possible to damage a loudspeaker by overdriving it with an underpowered amp for a sustained period of time (among other things). What are you hearing? Crackling in the tweeters? Metallic sound from the woofers?

They are NHT Classic 3, three way speaker.
When I first listened to them, the high was very detailed and pronounced. Now, some details in top high seem missing (I mean missing, not tamed). There's no crackles in the high, so it may not be cone problem; is it possible something melted, so no sound is produced for the top high? It would be easy to tell if they are two ways, but these speaker are three ways. Any one has a set of sound files to test different frequencies?

How did you break them in? By what method? (By the way...speakers don't need break in. Just use them, and after a few hours the woofer/mid suspensions will become slightly more compliant.) It sounds like you blew the tweeter.