It sounds like it's a Windows issue with that Discord app and possibly more. The Ubuntu test proves your audio chip on your Mobo is ok.
I would consider either rebuilding your W7 from scratch (W7 reset or W7 installation from factory Recovery Discs or Partition), or just bite the bullet and do a W7-->W10 upgrade which involves reinstalling all your programs from scratch and reintegrating your restored data from backup media. You probably realize this is not a 10 min. deal; and when I do this it typically
takes 2-3 weeks before you are back at 90% functional of where you are right now with that computer. Many people here and Clients have told me it can take up to 4 months to get everything working again. I have some Clients who have over 400 programs installed on their computers, and it can take forever to get every single one of them reinstalled
*finding the media discs or usb or download license keys etc.* You know what's involved and it sounds like you've done it before as have most of us, and you're right to fight shy of doing it.
At this point, you've got software issues, and you've proved your Mobo hardware and new hard drive are ok. If you can't do it this month, you might need to wait longer before you attack this, but keep in mind that there are a couple of issues that waiting will cause you to think about. The first is the
July 29th 2016 Anniversary of the free W10; so if you didn't have your W10 Activated (due to the crashes you mentioned and other problems such as the audio), you will need to tackle that and we don't know exactly how it will work until we do a few. 2nd, if you build your W10 system via upgrade or clean install on or after
Aug. 2nd 2016, that's the date Microsoft is going to release their
Anniversary Update to W10. Doubtless there will be issues and incompatibilities there that can also cause you further delay and frustration. I suggest if there is anyway you can get the W10 upgrade build done
BEFORE these 2 upcoming dates, you might want to do it. Getting your system working again with your audio problem fixed would be better to do than wait for after Aug. 2nd as if you wait and your audio stops working, you're going to be troubleshooting all over again and blaming those 2 events and updates for further failures. If you build it sooner, and take snapshot backup images and your sound fails after either the July 29th or August 2nd dates; you can just rollback via System Restore or Restored Backup Image prior to these 2 event-dates and get your system backup and running.
Another way to go would be if you need to wait past these dates to install, you can just buy a 2nd hard drive for your system and do the rebuild on the new hard drive post August 2nd. Ensure your issues such as sound and exception crashes have abated, and your good to go.
If after a few days or weeks of building the new W10 system on this new HDD something goes south, you can just pull that drive out, stick in your original HDD and be back up and running in a hour or so with the old build (no sound) to get you by for emergency access to your scheduled online events you to attend or running the various asundry programs you have all setup and configured for. When you get a couple of weeks of downtime, then you can stick that 2nd drive the new HDD back into your computer and do another complete rebuild of W10 and hopefully get it all working again. If that works, you can just stick the old HDD back in a drawer and just use it for emergencies if your new W10 build on new HDD ever goes out on you.
BBJ