Try right-clicking the speaker icon in the taskbar next to the clock, and choosing "Open Volume Mixer". This lets you adjust volume levels on a per-application basis, so e.g. if one application is too quiet you can turn it up, or vice versa. You can verify that the browser isn't set to zero this way (it may be necessary to have it attempting to play sound for it to show up in the volume mixer).
The leftmost column, "Device" also has a dropdown, and if you change the device there, it will show applications that are assigned to that device. This suggests that it's possible to have some applications going to one device (set of speakers, TV, etc.) and others going to another. I don't know how you change which device a program is assigned to. But if your browser is assigned to a device that isn't currently plugged in/turned on, that would also explain what you are observing.
Beyond that?

Never hurts to run a Malwarebytes scan, just in case. It does sound like an odd case.