So there's absolutely no way to trace an unavailable phone number?

The police can do it, but there’s no way the information would be passed to a member of the public. However if you are being harassed or called illegally, or a crime is being committed, report it to the police. They will be able to get the required information from the telephone company.

*69 used to call that number back if that is what you are looking to do.

There is unlisted and then there’s blocked.

*69 works in unlisted numbers. Some info-digging websites can get you (at least a partial) unlisted number.

Blocked numbers are almost completely invisible, except to law enforcement. You have to pay a decent monthly fee for a blocked number.

I have a blocked number.

My old office with 500+ employees displayed “Unavailable”. The number was not call blocked or restricted. It was just “Unavailable” because there were so many people calling through a main, in-house switchboard.

There is, but it has to be done through a cooperative effort with what’s known in telecommunications vernacular as the originating office.

Once the OO implements what’s known as an originating trap, information identifying calls to the number getting the calls will be entered in the call log generated by the trap. Once the incoming trap on the call recipient’s end determines the date and time of the specific call, then the calling (originating) number can be identified.

The Federak Communication Commission determines which phone company receives what numbers.

And, yes, the police have access to these cellphons numbers, by not civillians.

Befriend a police officer.
Become a police officer.
Subscribe to 2600 magazine. ;-)

Hire a skip-tracer/private investigartor

If you fail on whitepages.com or similar maybe fee-for-service sites usually listed on the directory site, such as intelius or peoplesmart can help you.
*69 or similar [see wikipedia info ] will call back and you can use some social engineering to find out who is bothering you when someone answers.