Probably not, as it seems you were deported for an aggravated felony... Try to consult with an attorney. You will need to show your full Immigration and Criminal cases.
Your green card was cancelled? This is not a simple question to be asked or answered on blogs. There are several issues, and it is a difficult case to win, from what you are stating. Consult with an attorney.
What did your immigration attorney say when you asked him/her this question? If you are not currently represented by one, you really should hire one as this is no simple matter that could be solved online.