What could this fictional kidnap hostage do?
There are a few problems with this scenario.
You said:
Imagine that one day a person wakes up in an unknown room with no windows.
After a few days he is informed that he has been kidnapped and is being held infinitely. — wax
The problem is psychologically how can any individual can tell the passage of time knowing minutes to hours, to days when there are no indicators that can mentally help the individual?
You also said:
He is given access to the internet, and the access is routed through the internet in such a way as to make any contact with anyone in the outside world, non-traceable.
There are things that could be done to sidestep this routing process. He could contact someone in the outside world, and then download some software that could access the computers real ISP number and send it back through the internet to the outside contact, but this process has been thought of by the kidnapper, and the ability to download software will have been disabled. — wax
This is assuming that the person is tech savvy not to mention you'd have to understand the current panic of the individual. Imagine a non-tech savvy person given the internet and not knowing how to work it?
It's a good start in grabbing the person but it have to be formed a little bit more realistic. Not trying to burst your bubble but it's a good start.