Xbox powers up but does not show picture

Starting a week or so ago my Xbox One S no longer appears to work. I can turn it on (the white Xbox button lights up), but it never send a signal to the TV. The fan will also start spinning (it was replaced a few months ago).

Whenever it's first plugged in, or when I a press the button after it sitting for a while, there is a faint beeping or buzzing sound coming from the Xbox. One short sound, then about a second of silence. It'll do that 8 times then have a longer break, and then start the sequence over again. After a while it stops doing it until you press the on button again.

It's pretty quiet but you can hear the beeping/buzzing in this video:

So far I've tried the following but with no luck:

• Full power reset (turn off for 30 seconds, unplug, etc)
• Hard reset using the power button
• Connect to different TV, using a different power cable and a different HDMI cable
• Booting into low resolution mode
• Pushing the eject button repeatedly when booting
• Inserting and ejecting discs while booting

Are there any other things I can try to troubleshoot what the issue is? I'm wondering if it's maybe the hard drive, but how would I be able to tell?