I want to know how I can trace a private IP address. I have been getting some harassing and slander e-mails from an {email address removed} account but the IP addresses on the header come out private. I want to be able to get a location, address, sender etc behind this e-mail so that I may proceed with harassment charges. Please Help

There is little to do unless the harassment reaches a criminal level then contact your local DA or police. Other wise you can report the incident to Google. The idea that you are going to gather information then sue or prosecute the offending party is flawed in the fact that if this is your goal the harassment needs to be documented by a third part for it to have any weight in court.
Report the incident to Google and or the authorities.

Even if you could get the IP, what do you think that will get you? The only sure info that will get you is the ISP that issued the address. And the only way to get further is with a court order.