From what I recall, that particular cartridge was always prone to glitching. When I was a kid I got through Dragon Warrior I, II, and IV without any problems, but never completed III due to the game always glitching in one way or another. I eventually tried a second copy with the same bad results.
My roommate was also playing it, and she was almost to the point I had been when I lost it (about 88% complete), so I copied hers, and finished from there. She finished with no problems.
The power outage didn’t affect hers, but hers wasn’t open.