Is it possible to hear absolutely nothing if you were in a totally sound proof room? I do understand that every bodily function would then seem to be amplified, but what is the sound of hearing nothing?
Note, that I’m not sure that this question actually makes any sense.
Yeah, deaf people hear absolutely nothing all the time. Ask one of them.
If you want to listen to your bodily functions, stick in some earplugs. You can do it on the cheap with your fingers. Not too far in, now!
You can rent out a professional recording studio for a few minutes if you’d like. I’m pretty sure they go by the hour though, and good isolation rooms aren’t cheap!
I think what the OP is asking is not, if I were deaf or had something blocking my ears, what would I hear. Rather, the question is: if I listen carefully in an enviroment without sound what would I hear. What would I be listening to?
You’d probably still hear air whistling through your nose 
I’ve been in an sound proof room in a court house, voices sound rather odd when deadened so.
I was in a sound proof corridor thing at the Ontario Science [del]Center[/del] Centre in Toronto years ago. Fun little walk.
Ears have an active feedback mechanism in the cochlea in order to amplify interesting sounds and deaden uninteresting ones (micro air movements, blood rushing, etc.). This system going out of whack can be one cause of tinnitus.
If you take away the background noise, for a while you will “hear” the uncancelled feedback in your ears. (I don’t know how long it takes for your ears to readjust.) In short, total silence sounds like low level noise.
You could sit in a vacuum chamber.
It’s really quiet and inky dark deep in a cave.
That was always my probelm with caves. It is indeed inky dark. If fact, I don’t think the word dark even begins to cover the amount of dark involved, but it was never what I would think of as quiet. Especially with all the screaming from the rest of the tour group because the lights were off.
I recall Rush Limbaugh commenting on hearing totally nothing if he turns off his cochlea implant, or the battery dies. He said it was strange going to total silence, but has it’s benefits as well. This is a bit different then the OP asked though.
Tour group? You gotta go in a wild cave, get all the inky darkness and total silence you want. You do hear occasional water drips in many places, depends on how wet the cave is.