Unfortunately, you have two very significant issues. The first is your criminal conviction. I presume from the sentence imposed, the crime was quite serious. United States immigration law is not forgiving when it comes to persons convicted of certain criminals convictions. If your crime falls into on of these categories, you may not be eligible to return.
The second issue is the attempted illegal re-entry. This subjects you to a bar to admission, which is often referred to as a "permanent bar". After 10 years outside the United States, you can request permission to reapply for admission.
You stated that you were an LPR. How did you obtain your status? Did you parents ever become United States citizens? If so, please provide the details of when this occurred and your age at the time. The reason I ask is you may have acquired U.S. citizenship and if so, you would be able to return to the United States despite your conviction and prior attempt to re-enter.
There is nothing you can do under current law to adjust your status.
The answer provided here is general in nature and does not take into account other factors that may need to be reviewed for a more precise answer. You should consult with an immigration attorney before taking any action. The answer here is not intended to create an attorney-client relationship.