Ah, I see now.
You tried entering your serial number?
As @JohnAtl says, the serial number would give you a better (but not necessarily unique) idea of what you have. I found this page useful, and this page tells where to find your serial number.
Also, you might try running Apple Hardware Test (AHT) on your machine. This page explains how.
I eventually identified the MacBookPro with the links provided and checked with the serial number.
It’s an early 2011 model. But even though, there are specifics between early 2011 models and I have to take care to find the correct replacement…
I extract it from the computer.
I checked on eBay. There are quite a lot of items for this MacBookPro. But some are dead boards (sold just for parts) and other are exchange only.
There are three A1286 machines listed for early 2011. It’s possible that a logic board for any of the three would work in your machine.
You have to ask yourself whether you are willing to gamble on a logic board of unknown provenance. In the US, (supposedly) working logic boards for your machine are listed on eBay in the $300 range.
There are really only two possible outcomes: 1) The logic board works; in this case you have a MBP that works and you got it for a fairly good price (assuming you originally got the machine cheap/free), or 2) The logic board doesn’t work; in this case you have an expensive doorstop.
It’s worth noting that the latest version of macOS that will run on this machine is 10.13 (High Sierra).
Yes, It’s that kind of reflections that I have right now. The cheapeast price (in Europe) I found on eBay is no less than $455 including expensive shipping asked by sellers. And it’s indeed a gamble.
So for the time being, I decided to wait…
The MacBook is in perfect condition (apart of that heavy problem, of course lol). It’s my former laptop. I bought a new one about one year ago and wanted now to refurbish this one for side projects. But for side projects it’s a prohibitive cost, even for a MacBook Pro and with the potential prospect of not having things to work properly with the replacement logic board.
Too bad but that’s where I’ll stand for now.