Your chances are slim to non-existent. Sorry. I know this isn't what you want to read but your criminal background will cause you to fail the background check.
You stated that you were able to get your conviction expunged . . . but this expungement does NOT apply for law enforcement positions. You are required to disclose every single previous arrest. You are required to explain (in detail) every single arrest. And you will be required to describe the final disposition. Your criminal charges - even if the prosecutor had declined to prosecute - would have created some serious problems for you. Your only hope of passing the criminal background check under those conditions would have been to pass the polygraph as you claimed you hadn't committed any offenses.
Your situation is that you committed a fairly serious criminal offense as a teenager - and you pled guilty to the harassment charge. If you were a police officer, this information WOULD get to the criminal defense attorneys. And criminal defense attorneys would absolutely annihilate you on the witness stand. Police officers who are lightning rods for defense attorneys will be very unlikely to make arrests that will actually stick. Prosecutors will decline to prosecute your cases.
Your diagnosis could also cause you problems - particularly if you attempted to conceal this information. There is no reason, per se, that someone with Asperger's Syndrome could not be a police officer as long as you were able to perform the duties and responsibilities and as long as you were able to work appropriately and professionally with the public, your peers and superiors.
Your past medications could be problematic, but you didn't identify them so I can't say for certain.
But just based on your criminal history, I just don't see you being able to pass the background check or the polygraph.