I'm not in the legal advice game, I just want to preface my remarks with that.

"Proving" the cause of engine failure in a case like yours is really, really tough. The facts as we know them: there was no oil in your crankcase, and there were no outward leaks. From there, we're not able to "assume" anything else as fact, but it might be reasonable to assume that the Valvoline store left your engine low on oil.

The counter argument would be: where did the oil go, then? It is possible that it burned through the engine without your knowledge. Modern catalysts reduce oil smoke to nothing, cars don't smoke like they used to when they burned oil. That oil consumption can be due to a number of factors, of course, but most commonly it's due to piston ring failure. But now that your engine is destroyed, it's a hard thing to disassemble it and "prove" that there was a failure present before the engine started coming undone.

The short answer is: in my experience, Valvoline sees a lot of claims like yours, and they pay a good number of them. The facts of the case aren't on your side, that is, you didn't drive away from Valvoline and have engine failure 30 minutes later. It was several thousand miles since they touched your car, and the only evidence you have is a ruined engine, which cannot be definitively pinpointed with regard to root cause of failure. It can't hurt to appeal their decision, but there is little point in having the local dealer disassemble and inspect the engine. We already know that the engine is ruined inside, it's doubtful that they would be able to point to any of those ruined components and say, "There's the culprit, they left it low at Valvoline." You might successfully argue the circumstantial evidence and win, but the physical evidence doesn't bear it out for me.

However, the flip side of this, again in my experience: small claims courts tend to rule in favor of the plaintiff and against the business owner in cases like this. If there is doubt to be cast, judges usually cast doubt on the business owner before the car owner. So, in that regard, you may have a successful day in small claims court suing the store owner (not Valvoline per se).

If the oil tech showed you the dipstick and it was full, then it seems that they did their job.... unless there was a loose filter or a loose drain plug, but you indicated that that's not the case.

An oil analysis at this point would indeed show oil breakdown..... because it did as the engine starved for lubricant and those surfaces overheated. What you're asking is: can they show retroactive breakdown, prior to the engine failure? Again, my experience is that they can test the oil you have on hand, which we already know to be destroyed. There's no way they can turn back time on that oil and see what it was like before the engine came apart.

I feel your frustration, but I don't think you're going to win this argument on technical points like this. I don't get the impression that you think the Valvoline store did anything wrong.... and they probably didn't. The impression I am getting is that you think your OIL failed, causing the engine failure. I can tell you that, from an insider's perspective, that's one of the best jokes going in the business: Valvoline warrantees your engine against oil breakdown failure, which is nearly impossible to prove out. I don't know that Valvoline has EVER paid a claim on that warranty.

Valvoline makes a fine product, and I doubt that their oil quality was the root cause of your problem. The analysis seems to be that your engine ran low on oil, it didn't leak out, we don't know why it apparently burned out of the engine, but I think a judge would say that the onus is on the car owner to make sure the engine stays full of oil (for example, the owner's manual recommends checking the oil level at each fuel fillup).