If the broken instruments were recently discovered then you should have no problem bringing a claim. Otherwise there may be statutory problems. We have handled many similar claims.
The general rule for dental malpractice claims is 2 1/2 yers from the date of malpractice/negligence. The statute dealing with dental malpractice claims provides the following, "An action for medical, dental or podiatric malpractice must be commenced within two years and six months of the act, omission or failure complained of or last treatment where there is continuous treatment for the same illness, injury or condition which gave rise to the said act, omission or failure; provided, however, that where the action is based upon the discovery of a foreign object in the body of the patient, the action may be commenced within one year of the date of such discovery or of the date of discovery of facts which would reasonably lead to such discovery, whichever is earlier. For the purpose of this section the term “continuous treatment” shall not include examinations undertaken at the request of the patient for the sole purpose of ascertaining the state of the patient's condition. For the purpose of this section the term “foreign object” shall not include a chemical compound, fixation device or prosthetic aid or device."
Your claim may be viable under the "foreign object" exception--:the action may be commenced within one year of the date of such discovery or of the date of discovery of facts which would reasonably lead to such discovery, whichever is earlier.
When was the needle discovered? If within the past year, may have a claim. Could it have been discovered earlier? If so, the claim may be time-barred.
You need to consult with an attorney and get more information to know if you have a claim.
Initially, any dental malpractice claim has to be brought within 2.5 years of the date of the act of alleged malpractice, as a general rule. Clearly, that time period has passed in your situtation. However, NY does have limited "discovery rule", which applies to claims of injuries due to "foreign objects" left in the body, which should not have been - in which case the S.O.L. would not run until when that circumstance was discovered, or reasonably should have been discovered. There are insufficient details provided to allow determination as to whether you can take advantage of the "discovery rule". However, your brief post raises a general question as to whether there was actionable malpractice, to begin with. That requires a showing not only of an act of professional negligence, but also that said negligent act caused you an injury that you would not have otherwise suffered if properly treated, or of a definable worsening of an injury or condition that you would not have otherwise suffered. Notwithstanding the fact of pieces of needles being left in the canal, you post again does not lead automatically to such a finding. Consullt with a dental malpractice attorney in your areas- but it will llkely be helpful if you first get your records and films from the prior dentist and your present one.