You should first look for counsel to review all your post-conviction relief options.
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Regarding the VOP and the dropping of the charges, I would not always agree with what you have been told. In Georgia, (read different than NY maybe), there is a different burden of proof for VOPs and traditional criminal trials. Many times the charges are dropped but the VOP goes forward.
I am an appeals lawyer in Albany, New York -- you are going to have a difficult time getting this heard by an appellate court due to the fact that you likely waived your right to appeal at sentencing and failed to file a notice of appeal w/in 30 days of the judgment of conviction. HOWEVER, you may very well be able to secure relief in a CPL 440 motion - this is a post-conviction motion that is heard in the court of first instance -- here, whatever town court you were convicted in. This motion may well be meritorious and should be immediately explored.
It is likely too late to appeal. You need to do a 440 motion based on ineffective assistance of counsel. You need to start by doing a foil request to the police and DA for the video. You have an uphill fight. I suggest you retain a criminal defense lawyer.
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It is highly unlikely the "Dash-Cam" video has been preserved. These are usually kept for a short period of time and then erased.
As my colleagues suggest, your options at this point are limited. I do not know of any vehicle to allow you file an appeal at his date. You would have to file an application for leave to extend the time in which to appeal. I doubt the court would entertain it.