If a direct appeal process and the state post-conviction process both fail, are there any other legal avenues?

Yes, there is another important legal avenue and that is seeking a writ of habeas corpus in federal court. Habeas corpus is a Latin term literally meaning you have the body. In a writ of habeas corpus, a defendant collaterally challenges his underlying conviction (often in state court), alleging that there were constitutional violations committed during his trial.

For example, a defendant may allege that his underlying conviction should be overturned because his Sixth Amendment right to receive assistance of counsel was denied. This is often called an ineffective assistance of counsel claim. Or the defendant may show that the prosecution unlawfully refused to disclose exculpatory evidence over to the defendant’s attorney. Or the defendant may contend that the trial judge violated the defendant’s due-process rights by holding the proceedings in a manner fundamentally unfair to the defendant.