Law enforcement officers can obtain information with a search warrant, which is a document issued by a judge or magistrate that authorizes them to search for specific information or evidence based on "probable cause" to believe that it will inform the investigation or prosecution of a crime.
A court can also issue a subpoena at the request of a party to a proceeding before it. Since in most cases only the state can bring criminal charges before a court, an individual would have to bring a civil complaint before a court in order to even request a subpoena related to his complaint. Also, it is up to the court to enforce its subpoenas: It's not like a warrant where you can then pursue the items subpoenaed through force. If the subject of a subpoena doesn't respond you have to ask the court to compel the party, which means you have to bring your complaint before a court that has jurisdiction over the party you wish to subpoena. This can be difficult when it involves a third party – especially a third party that would rather ignore or object to the subpoena than hand over the information.
I.e., if you can't convince law enforcement to investigate the crime, and you can't convince the company in possession of the data that it's in its interest to help you, then you would most likely be facing a steep legal bill to get an attorney to successfully obtain the information through civil process.