You are correct, the realtek audio device (speakers) are not currently my default playback device. Unfortunately the option to make them the default device is grayed out. What does this mean?
Unless the integrated audio option got disabled in BIOS, it sounds like your audio chip may have bit the dust. Go into BIOS at start up and look for the enable/disable option for the audio.
You could try one more thing. Uninstall the integrated driver again, run Driver Sweeper from Safe Mode, have it remove any audio driver remnants that got left behind. Re-boot and see if Windows recognizes the audio chip and loads a default driver. If Windows doesn't recognize the chip (but it has in the past), then I'd say the chip has failed.
Driver Sweeper: http://phyxion.net/item/driver-sweeper.html