No, there is no option in BIOS to disable Windows sounds... all you can do there is enable or disable your onboard audio completely. Disabling the Windows Audio service will also result in all sound being disabled. I think the OP is looking only to disable Windows sounds... after all if you didn't want any sound at all, the easiest option is to simply unplug the speakers or headphones.
If you select "No Sounds" as your sound theme it goes back to "Windows Default" all on it's own? If that's the case either your sound driver or some other piece of software wants you to hear all the Windows sounds... whether you want to or not. I'm using Windows 7 and just selected "No Sounds" and it stuck. My best guess is third-party software or even malware is causing your issue. That is, unless you're trying to create your own custom sound scheme... and if that is the case, you MUST save your sound scheme when you make changes, otherwise all your changes are lost when you close the applet.