My car broke down and dealership is now blaming the oil change for the failed engine. Car is in perfectly good condiction. Please HELP!

I drive a 2011 Lincoln that has 40,000 miles. The car is in perfectly good condition and I had a routine oil change 1,500 miles ago. After going out of town and driving 200 miles, my car broke down. The Ford dealership I had it towed to charged $600 to inspect the engine and are claiming there is zero oil in my car. They also said they could not find any leaks or malfunctions. As such, they are blaming the oil change place I went to (not a dealership and lesson learned). The dealership told me they have video footage of filling my car up with oil. Who is to blame? Ford is charging me 8,000 to repair my engine and says they will not cover it since it is the oil change places fault. What do I do? Do not have 8,000 to spend. This is completely unfair as I have done my due diligence to ensure my car is properly taken care of.