Well, it's not uncommon for the hit-and-run vehicle and driver to be unknown, so not knowing the license shouldn't be a factor. But I'm confused by the "if you are At Fault" part of your question. Do you mean that you did the hitting but the other driver ran? Doesn't really matter, I guess. If you have collision and comprehensive insurance, it should pay the claim. If you have only liability insurance, you don't get anything.
As long as you have collision coverage
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