That's really odd. This is the first I have heard of someone having an issue by following the exact process of the "how to" video and also having a checksum that is good. Do you have the latest version of Mesen?
There are a couple of other things you can try out. First, you could attempt manual installation. To do this, follow the process below (it's a little more complicated):
-Create a folder called "HdPacks" in the same location as the Mesen.exe file.
-Inside that folder, create another folder with a name that is identical to your ROM.
-Download the HD pack and unzip it somewhere.
-If you browse inside what you just unzipped, you will find another zip file (a zip within a zip).
-Unzip that second zip somewhere and move all of the contents to that folder you created that matches the name of your ROM.
-When finished, you should have a folder inside your HdPacks folder that has a name identical to your ROM. Inside that should be many .ogg files and .png files.
-Try starting the game and see if it works.
If that fails, you could also try manually patching the ROM you have with the Metroid mOTHER .ips file using Lunar IPS (Metorid mOTHER is available at https://www.romhacking.net/hacks/1988/
). Try following the manual install process above with the patched ROM instead. If it boots up, congratulations - you are halfway there. From here, all you need to do is find the hires.txt file inside the HDPack. Use ctrl+find. There should be two areas where a checksum is listed (ecf39ec5a33e6a6f832f03e8ffc61c5d53f4f90b). If you replace that existing value with 607b429388c1652f3194dfe599e6355dd7d59967 the sound should now be working.
Lastly, you could also try Retroarch as well since the newest cores that are available have a version of Mesen compatible with the pack.
Hoping something sticks here. Let me know if any of this works.