I think you will, justifiably, be hard-pressed to get the W HNL to take responsibility for this.

Sometime between the time you picked up the car at the airport and when you returned it, the car got damaged. You think the only place it could have reasonably happened was at the W, but there's no way to be sure of that.

Since you didn't say, at the time, that when you gave the car to the valet, it was not damaged, and when you re-claimed it, it was damaged, I think it will be a real stretch to make that case now. Reports are that it is hard enough to get hotels to take responsibility for these situations when you do address it at the time. I think your chances are even slimmer in this case.

Personally, if I were in your shoes, and couldn't be certain of when and where it happened, I'd pay the bill or, if it ends up being a lot of money, get my insurance involved.