You most certainly can file a PCR Petition in Indiana and, if your previous public defender admits to the facts you have outlined, you might have a chance of having your petition granted. If you agreed to a plea and your counsel failed to submit the signed acceptance of that plea before the offer was revoked, a judge might consider that to be ineffective assistance of counsel. If you signed a plea, your right to appeal was probably waived in the plea agreement. However, that does not prevent you from filing a petition for post-conviction relief based upon a violation of your constitutional right to effective counsel.
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You would have had, but I believe the time to file for PCR would have run years ago. I would recommend checking with a local criminal lawyer to verify what the time limits are in your area, but I know of none that are open for over 6 years. Hope that's helpful