Power cuts, I assume you mean the power goes out unexpectedly and your system shuts down improperly. That could corrupt the Library’s database. A small, cheap UPS battery backup would help a lot.
First, in the Viewer menu, verify you are set to use Original/Optimized Media and not Proxy Media. I’m going to guess you’re set to Proxy media there, IF the Library is not corrupted from the power outs.
If it is the power outs, go to your FCPX backups, open some of those, see if they’re still in tact.
Dragging back into the Browser, no, that’s not the way to do it, won’t work, as you’ve seen.
When you go to Relink, you can chose for FCPX to show you unlinked media, or select it to show you all media, set it to all, do you see a list of anything?