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I am sorry to learn of this situation.
The Puerto Rican Government (in association with the U.S. Government) has been addressing widespread fraud with regard to individuals using PR birth certificates as a way to facilitate identity fraud).
This has led to complications for citizens such as yourself in getting their passports.
(This is discussed in detail here: http://www2.pr.gov/prgovEN/Pages/BirthCertifcateInfo.aspx#faq).
The resolution is straightforward, it will cost you a small fee and take a short amount of time. You will have to purchase a new birth certificate (ordered through "VitalCheck" (the provider that acts as the clearinghouse for records such as birth certificates for Puerto Rico (as well as many other jurisdictions) - again, this information is confirmed in the PR.Gov website above, and you can find the VitalCheck site here: https://www.vitalchek.com/
Make sure when you order the certificate that you order a "Certified" birth certificate.