List of compatible motherboards?

Ok, to make a long story short. About two months ago I pulled a Kyle and spilled some of my Old Rasputin on my laptop. Immediately unplugged everything and disassembled to let all components dry.

Flash forward to today. Reassembled and operating, upon boot up I’m told the RTC Battery is low. I don’t have a multimeter on hand to check the terminal voltage. So I’m assuming the RTC Battery is either dead or near dead. Lovely.

My question however is simply this. Since I’m going to be digging around in this thing for a little bit. Is there a website or resource available that list all compatible motherboards with the C55t series laptops from Toshiba?
I’m assuming I have a variant of the LA-B301P Intel i3-4005U.

The RTC/CMOS battery is normally a simple CR2032, you shouldn't need to get a new motherboard. It should be somewhere by the SATA connector for your hard drive

I meant to specify. I'm wanting to place a new MB in the laptop. I get, "inspired" to tinker every now and than.