Proving access. Even if you can prove that you wrote the words -- for example, you kept a notebook for 39 years documenting your poetry -- you still must prove that the musician received your words (in copyright parlance, that's referred to as "access") and copied them. That seems like an awfully difficult thing to prove. The affidavit from your friend is good but unless she can verify that the pop musician actually received your letter, it won't help your case very much. In summary, it's not out of the question, but proving infringement will require hiring a lawyer and taking a financial risk.
The passage of time. You say that you discovered the infringement in 2007. The Dear Rich Staff researched online music stores and found copies of the recording dating back to 2002. If you do go to battle against Mr. PopStar, you will be grilled as to why it took you so long to discover the claim, and then why you've waited two years since discovering it to do anything about it. Perhaps you have good reasons for this -- you were ill, you had personal problems -- but courts disfavor people who sit on their claims.
Statute of limitations. Finally there's the statute of limitations -- a copyright owner has three years to take action from the date when they learn of an infringement (or should have reasonably learned of it). In the case of an active infringement such as this, your claim will likely be limited to the three years preceding your filing -- for example, only the revenue earned by the song between 2006 and the present. If you feel strongly about this ripoff, we recommend that you contact a copyright attorney for more advice. If you have sufficient proof, you may be able to find one who will act on a contingency basis. If you live near a major city that has an arts-lawyer service such as California Lawyers for the Arts, you may be able to obtain low cost legal assistance.