Please stop posting the same question. Consult an appellate attorney in your area. No one can give you accurate feedback based on this information. They would have to read the entire record in the case.
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Please refer your question to a post-conviction appeal specialist. It's impossible to answer your question without a full and objective investigation of the facts and circumstances surrounding your case. Additionally, I'm always suspect when someone says their lawyer "did nothing." Defense lawyers rarely do nothing. Most of the time their actions are limited by the facts, over which they had no control.
In your post you said, "the jury should not have been able to convict based on the accomplice’s testimony alone."
I would assume the State did not call that one witness, then rest their case. If there was other evidence introduced, such as the crime scene evidence, autopsy, etc., then the conviction was not a result of the accomplice's testimony alone, but that testimony together with the rest of the evidence.