Is there a way to find out who the private calls are coming from on my cell phone?

I really don't think there is.
I don't bother answering calls that block their number

I've had the same problem and tried everything to identify the blocked calls, so far I've come up with nothing.

Just don't answer. The way I see it, if they don't want me to know who they are then I don't want to talk to them. :)

On my land line I have a option that forces the person calling to enter their number. If they don't, the call doesn't go through.

Sadly it's not foolproof, they can enter any number they want, as long as it's a 7 digit number.