Oh man... you are not going to believe what happened to me.
So I found out how to bypass the security in the system32 folder and renamed the winmm.dll file. Nothing bad happened at first and Settlers 3 still didn't work. Then I spied the correct winmm.dll file and renamed it but Settlers 3 still didn't work. Actually, nothing was working except for basic open / close folders.
"Oh shoot," I thought to myself, "the system32 winmm.dll must have been important to run Windows! I better go and change it back."
So I went back to rename the file but it wouldn't rename.
"That's strange," I thought to myself again, "I wonder if it will change if I take it out of the system32 folder."
So I took it out and was able to rename it. Hurray! Except now it wouldn't go back into the system32 folder and I kept noticing new Windows functions that weren't working anymore. I was able to find a video explaining how to get control of the system32 folder which may have helped me fix things but the video went black and my computer died.
Restart?
Nope, Windows launching crashed into a dead black screen.
Use F8 or Shift+F8 for diagnostics mode?
Nope, Windows 10 boots too fast for that.
Phone Windows Help desk?
Nope, 2 hour wait time.
Use boot discs?
Nope, lost them...
Eventually I found an answer. Create a Windows 10 boot media with a zip drive on my wife's computer and use it to reset Windows on mine. The reset got me started again and then four hours after I attempted Microsoft help desk they called me back (read: 2 hours after the 2 hour estimated wait time) to see what I needed. Lost all my software and it's taken me two days to get most of it back.
But yes, now that Windows is reset I employed the renaming fix for the correct winmm.dll file and the game works well. Miss the music though.