I want to make sure that I am clear on this question. You were adopted by one man and he has died. Did the second man adopt you after the first man died or before? If you were the legal child of the first man at the time of his death, you would be entitled to some of his estate. If you had already been adopted by the second man, the answer would be no.
This information is provided as a public service to provide a general answer and should not be relied upon as legal advice.
When a person dies without a will, their probate property would pass to the surviving spouse, if any and children. However, I would agree with my colleague. If you were adopted before your biological father died, you do not have a right to inherit from your biological father as the adoption would cut off your right of inheritance. You would be considered as the child of your adoptive father and could inherit from the adoptive father but not your biological father unless he made a will, which you say he did not do. If you were adopted after your biological father died, then you do have a right to inherit from both your biological and adoptive fathers. So its important to get the order of the dates of death and adoption correct.
You indicate that your biological father died. When did he die and where did he live at the time of his death? Was your biological father married, i.e., did he have a wife who was alive at the time of his death? Were there any other children of your father? What assets did your biological father own, if you know?
Assuming that you would be entitled to share in any probate estate, you need to contact the probate court in the county/state where your biological father lived at the time of his death. Contact the court at least 30 days or more after death as it may be too soon for an estate to have been opened prior to that. While there is no will, any administrator (like a wife or other child) will file for letters of administration and a preliminary inventory of assets (possibiy). Some states also require any heirs to be given notice, but it would depend on when you were adopted. I would make a copy of any documents in the file and consult a probate attorney who practices in the county where the estate would be pending to see whether you can inherit and what you might get.
If no estate was probated, it can mean a number of things - (1) that there are no probate assets justifying probate; or (2) the family/next of kin do not realize that they should probate an estate. If more than 6 months have elapsed since your biological father's death and there is no probate, then anyone can seek to do so and maybe you would wish to undertake that responsibility if you would be entitled to a share of any assets.