No, the noise does not sound like it comes from inside the freezer. It sounds like it comes from the back/bottom of the appliance, probably where the compressor is. And no, the noise does not stop when I open either the freezer or frig doors.
I don't see a fan at all. This is a picture of the back where the noise seems to be coming from: http://tinyurl.com/bzwqv6v
The big black thing in the middle, which I assume is the compressor (and happens to be very hot), is where the noise seems to be coming from, but there is no 'fan' that I see.
It's about 8.5 years so probably well out of warranty. Here is a recording of the noise again (http://tinyurl.com/afdg22y); at about 15 seconds into the recording I switch off the power at the wall and you can here something spinning down. I assume that that is the motor inside the compressor coming to a stop. Correct?