LAPD Appeal Denied - What Now?

I have a question regarding what happens after the review panel has seen an appeal and denies it. Let me give some insight as how I got to this point. I have been going through the hiring process with LA City since Dec 09, experiencing various delays along the way but I remained dedicated to the process. I have been successful throughout the entire process up until my psych interview when it was determined that I neglected to mention a previous work injury (approx 10 years ago) during my medical evaluation. My medical appointment was before I even had a sit down meeting with my BI, so from a medical standpoint I don't even think of this injury simply because it has been non issue for almost 9 years. When I met with my BI I did disclose the work injury to account for time out of work and workers comp payments received. The Background department checked into the injury and my claim against my previous employer and deemed it to be legitimet and cleared me from the background process. My medical exam went flawlessly, they would have never known I had the injury if I didn't mention it; I passed all aspects of their testing components. As a result, I appealed this decision to remove me from the process; they based their initial decision on a concern of my integrity. With my appeal I submitted approx 13 letters of recommendation / referrence from friends in various occupations ranging from police officers to doctors and city attorneys - there was even one from the Govenor's office. My oversight of mentioning this work injury during my medical process was not an intention to decieve in any way, it just is something that is far from my mind - medically speaking. Perhaps if I had the interview with my BI first it would have been more in the front of my mind since I disclosed it to them. Ok, here's my question - if the appeal was denied how do you keep fighting? I'm a firm believer that if something is worth having it is absolutely worth fighting for. I'm fighting for my career and a better life for my family so I have every incentive to push as much as I can. The interesting part about this is the background department is on my side, they believe this to be a technicality that medical services decided to blow up unnecessarily. I'm willing to do whatever, write to whoever, I just need some advise and direction. Any help anyone can provide will be greatly appreciated. Thank you in advance for your time and help.