Logic Board Part No

This issue is definitely related to the logic board. There is definitely damage to the board from the liquid spill and likely ESD damage from when you replaced the MagSafe board.

There is no supported way to replace or find a temperature sensor on your model MacBook Pro. In order to replace a sensor on one of these boards you'd have to solder off the old one and solder on a new one. Since no one sells temperature sensors for the boards that integrate them, it would be a nearly impossible feat.

I'd recommend taking it to the Apple Store or an Apple Authorized Service Provider for a full repair. They may not be able to service it since you've serviced your own machine.

I know this isn't the news you were hoping for, but I hope it helps.

Since you've paid for AppleCare - send it in. It doesn't make sense you would be charged for a repair unless there was some sort of external damage, so perhaps you misunderstand the quote.

Perhaps the pricing was for an estimate if the fault was not covered so you could be prepared in case that were the case.

Call back and ask to have your situation cleared up or drop by a store with if one with a Genius Bar is convenient. I would remove the third party RAM and accessories (as Apple will ask you and inspect for before beginning service) before presenting your Mac for service. Inform them you have had a second drive in the optibay and offer to let them have / evaluate the part if desired to ensure it didn't cause the malfunction.

Here are the North American terms of service - and you can see that Apple may charge you a diagnostic fee if you send them a Mac and the failure is due to third party parts being the cause.