It would be the best situation if your father had signed either (1) a living will; or (2) a health care proxy; or (3) an advanced health care directive under the federal Personal Health Responsibilities Act or under New York State law (or the law of a state that a particular person resides as a general rule). Each of these documents would most likely be suitable to support your request to obtain and review the medical records of your father. This is true in most cases even if those documents do not contain specific language referencing HIPAA--the federal health insurance protability and privacy laws.
The fact that you may have a general financial power of attorney may be partially helpful to you to a more limited extent. Under standard New York power of attorneys, you do have the right to handle medical billing matters on behalf of your father. The provision concerning "personal and family maintenance" matters may be of some help and you can argue it but it is not controlling in your situation.
Finally, if your father has some lucid moments, perhaps he could issue a written extensive advanced health care directive, living will and proxy to you--we recommend two independent witnesses and a notary public in such instances: such a document would help you a lot. Try to make sure that your whole family is on board--your siblings, etc. And be sure to consult with an attorney who practices in this area as either an estate planning or elder law practioner. Good luck to your father and to you in this very trying situation.
This answer does not constitute legal advice in any form ; you have to meet and consult with an attorney on this matter.
you can try it with the doctor's office, but technically the power of attorney does not relate to health care matters. you do not mention if your father signed a health care proxy, which would be sufficient for HIPAA purposes.