If you have been a lawful permanent resident (green card holder) for three years, and you adjusted your status through your marriage to a U.S. citizen, you can file an N-400 and apply for naturalization. You also have to meet other eligibility criteria to obtain citizenship; check the USCIS website for more information regarding filing your N-400: www.uscis.gov/n-400. You may want to seek advice and representation from an experienced immigration attorney, they can advise you further regarding the application and interview process, and assist you in this matter.
The statutory period begins when you were actually adjusted so it appears that you are eligible to apply for naturalization now , assuming you are otherwise eligible and meet all the various requirements. You may actually have been able to apply after only 3 years from the date of adj. if you were married to a US citizen and met other requirements. The fact you were delayed prior to 2008 due to name check issues does not affect the statutory period of 3 or 5 years. In any event seek help from competent counsel and they can discuss with you your eligibility for naturalization. Good luck.
No attorney-client relationship is created or implied by this communication.
On your resident card is the date you became a lawful resident. You may apply 90 days prior to having five years as a lawful permanent resident under the five-year rule. You may apply under the three-year rule 90 days prior to having three years as a permanent resident. But start with the date on your resident card.
Attorney Robert Brown's (former INS Director, 1972-99) reply to your question is general in nature, and does not constitute legal advice as all facts are known to him. For specific advice or representation you should retain an attorney experienced in immigration law. Mr. Brown's reply on AVVO does not create an attorney/client relationship not constitute legal advice.