Well, you are quite right, Sound 36 in KQ3 is definitely odd! I looked at it closer, and discovered that it IS a valid resource, at least in the sense that the entry in the SNDDIR file does in fact point to a resource in VOL.1 that can be loaded by the MSDOS interpreter. Track 0 of that resource is what you hear in the game (as you described).
HOWEVER, that resource has bad pointers for tracks 1, 2, and 3. All three of those tracks have starting and/or ending locations well beyond the end of the resource, meaning they don't point to any valid data. Track 0 is 757 bytes long (151 5-byte notes, with trailing FF-FF marker). But the resource is 1035 bytes long. There are ~280 bytes of extra data; they contain notes that are nearly identical to the first 48 notes of track 0, but with slightly different duration and volume settings. I'd guess it's remnants of a previous version of the sound.
Logic 7 is where that sound gets used. It works in MSDOS because only track 0 is played. The bad data for the other tracks are never accessed so you never know there's a problem. The Sierra interpreter is full of examples where badly formatted resources run OK due to bugs and such.
WinAGI detects the bad track data and assumes the sound is no good. That's why it gives the invalid resource error. I assumed the error was an invalid pointer in SNDDIR (there are several Sierra games where I've seen that) but turns out I was wrong! Now that I understand what's going on I can update WinAGI to better handle this situation.
The only workaround I can suggest is to not do a full game compile; if you just compile dirty logics, the other resources (pics, views, sounds) are left alone. Or you could manually extract the resource from the VOL file, fix it in a hex editor, then import it back into sound 36. Or, you can just use the repaired sound file that I've attached to this thread. I'll make it a priority to do some kind of patch in the next version of WinAGI that can deal with this problem.
You also helped me find another bug in WinAGI - when compiling, all ResourceIDs are stored in a list so they can be used as defines. But when a resource gets deleted, its ResourceID isn't removed from the list. That leads to the odd behavior you are seeing. I'll fix that for the next version.
TL-DR:
Sound 36 is definitely needed in KQ3. It works in original MSDOS interpreter even though it has bad data in it. WinAGI sees the bad data and considers it an invalid resource. I need to update WinAGI to allow corrupt sounds as long as there's enough good data to play in MSDOS. A repaired version of Sound 36 is attached that you can use to continue working on the game in WinAGI current version.