Is their any hope to sue for medical malpractice now that our son is 15 and his injury happened at birth?
It is highly unlikely that you could successfully sue at this point. First, there is something called a "statute of limitations," which defines how long you have to sue. If you wait too long, you may not bring a lawsuit. The statute of limitations, or SOL, varies by what you are suing for and state, but in Arizona, for example, for medical malpractice, it is only two years after the injury, or at most two years after the injury occured. After 15 years, it is almost certainly too late: while there are some theories or concepts that can "toll," or extend, the SOL, they are unlike to extend it this long.
Second, after so much time, as you are discovering, it is very unlikely that you can find the evidence and records you need to successfully bring a lawsuit. Without sufficient evidence, there is no point in suing--you would not be able to win your case.