My suggestion is that without delay, take advantage of any eBay or PayPal protections offered, there's been a couple of times I've used eBay protection & another time with PayPal that didn't involve an eBay transaction. While there are many honest eBay sellers, there's a few shady ones also, that gives the site a bad rap.
There has been times when I bought computer related components on eBay, all of the new items were fine. The few used or refurbished ones, were a mixed bag. I've had couple of refunds & a few replacements, as well as tossed a couple that were no longer covered, though this has been some time back. The last used item that I bought was a hard drive, back when the previews of Windows 8 was announced, for that purpose, to test the preview with, as new ones were costly in early 2012. It clicks at startup & shutdown, otherwise ran OK. But that's my last used HDD.
There are some items where eBay isn't the place to go for & used MB's is one of those. Yes I know they're hard to find, but with some extensive searching, many can be found outside of eBay, where you'll get some form of warranty, if nothing else, 14 to 30 days. It is too much work involved to be dealing with components of unknown usability. Many of these sellers says they're tested, but this can & should be taken with a grain of salt. These sellers buys up lots of non-working computers, strips all of the components & lists what they think may be good at high profit margins.
Some of these "lots" or bundles of computers can be bought direct from the eBay site.
I've replaced many components on notebooks, but the motherboard hasn't been one of those & this is why. At today's prices for refurbished computers, many with a warranty, with the option to purchase up to two extra years, it's often best to go that route, or a new budget model from online or local retailers.
Too, if the OS is the one that shipped with the computer, it lives & dies with the motherboard. Though sometimes MS will re-activate the OS, at their discretion, they don't have to & it can hinge on whatever mood the rep is in on that day. Seriously. I was given the run around transferring one of my Windows 8 Pro upgrade OS's to a working computer, even though it's in the EULA that it can be moved, as long as the same conditions were met (a previous Genuine Windows version installed).
So that's a concern also, if this is an OEM install. If a full retail version, no problem.
However at the moment, I feel that you should seek whatever purchase protection that you have & get refunded for this bad component. You've lost what sounds to be a lot of time with this, shouldn't lost your money along with it.
Hopefully you will be refunded, even if it takes filing a claim, which you'll likely have to do.