Dell tech support claims bogus "spillage" voids warranty

I recently returned my 3-year old Dell laptop for repair; the warranty expires in 7 days. It simply wouldn't boot up or power on one day after I left it on overnight, an issue I've had consistently since taking it out of the box. I was always able to get it back on eventually but not this time. My only recourse was to contact technical support - no in-house support where I live.

The first return-shipping box arrived within 3 days of my initial 30 minute call but it was missing the return shipping label. Another 30+ minute phone call, several emails, and two weeks later, the second return-shipping box with the shipping label arrived. Fortunately I have another laptop to continue working on during the span of those  2 weeks.

This morning I received a phone call at 6:45 am followed by an email from Dell Tech Support stating that the repair is not covered under warranty because of "(spillage damaged)Motherboard, keyboard, palm rest" and the cost to repair will be $359. How convenient and utterly unfounded. This laptop has spent it's 3-year life on a laptop stand, 4 inches above my desktop with an external keyboard and mouse. I've not used the keyboard/mouse/palm rest nor do I allow liquids of any kind in my work space (lots of paper). I disputed the diagnosis and asked to whom I could escalate the issue and was told photos of the "damage" would be forthcoming in 1-2 business days. Until then the repair is on hold.

It took me less than 5 minutes on this message board to find others complaining about "spillage" - i.e. non-warranty - diagnoses. I KNOW no liquid has spilled on this laptop and I consider tech support's insistence that there has been, a default response. I am not satisfied with Dell's tech support response and have zero faith in their integrity to now resolve what should be a minor issue to my satisfaction.

To whom can I file a complaint?