I think the problem is that I can't find a Quest of Ki rom headered or unheadered in GoodNES, NonGoodNES, and No-Intro that matches this rom information:
File: Quest of Ki, The (J).nes
Length: 196624 Bytes (1 Mbit)
MD5: 36DE069D 2DF3DE4F B9B2E2AF 9AF077CE
SHA1: 8F02CDD9 9AD4B27A 85EF1208 A9520B0C 1734F608
I tried patching Quest of Ki, The (J).nes from GoodNES, both headered and unheadered with Beat. In both cases the patching failed.