It seems, that I might be an idiot. They didn't sound entirely like post beeps and I shouldn't have labeled the post as such. They were actually coming from an old Seagate HDD. Apparently it failed and I didn't notice because it was just there as backup storage. It was making that noise every time I started. I don't know if it was generating a noise as a warning, or if it was just a noise it was making internally. I had to take the side off my computer and stick my head in there to realize it wasn't coming from the onboard speaker. Also realized at that time that the noise stopped as soon as the HDD led started blinking.