Hello! I tried connecting my board but it just doesn't want to, I am using the blue arduino Uno R3 and I tested with another board, and the other board works, I don't know what to do, the only visible difference is this!
Not clear to me, sorry.
First of all, you need to clarify what you mean with "it just doesn't want to": to do what? To connect to your PC? Or it connects to the COM port (aka. the COM port appears) but you can't open it? And on which operating system, windows or...?
Second, the Serial device is managed by a specific USB-to-serial driver, so if the problem is the COM port not popping up when connecting the board, you could/should check the serial chip of the two boards, I think they're different so you need to install the proper device driver (e.g. CH340 or 16U2 or...).
The top board is a clone. Get a magnifying glass and determine what chip is being used for the USB/Serial connection then install that driver.
Op has the "blue" board, and states the top board (Elegoo) works (probably has CH340/341 - that was what I needed for my Elegoo R3). "Blue" board probably is a clone, might have a different comm IC, and maybe the no-labeled 328p has no bootloader.
Try swapping the Atmel CPU chips. It could be bad or as xfpd says, maybe it's not programmed with the bootloader.
Check the official documentation regarding what chip is used for the USB/Serial and bootloader, it is NOT the MCU. ATMega16U2 is the chip I know for a REAL UNO, but I don't think it has a real UNO.
I try to connect it to my chromebook through the usb port using a blue connection cable, but the black board shows me a message of connection when I plug it in, not the blue one, the blue one is the one I used for the past year, and it was working FINE until a week ago, I tried everything, so I came here to get maybe answers, the blue board has a white "belly":
and the black board, a black "belly":
both board are using ATMEL ATMEGA328P and ATMEGA16U2 chips
the cpu chips are the long ones or the small square ones?
On these boards, the long ones. The square ones are the 16U2 you said both have...
Any clue on what circuit was on the board a week ago?
can you precise by what you meant with "circuit"
but alright, I will try to change them
I have changed both, tried both, only the black one works, again
What else (sensors, LEDs) was connected to the board that may have burned it.
If the black one works with the MEGA328P that was on the blue board, we can conclude that the blue board is bricked. I guess this was what @DVDdoug wanted to know.
nothing was plugged in, that I remember
the only things I plug in are always re-checked to see if it could make any short circuit, so I don't know what could have broken it
Ok. We all have been to this point some time in our lives... 
Unless someone else has a better idea, get yourself a new Uno. This blue one is a goner. You can keep the 328P for the future.
ouch.. alright, thanks a whole lot for the help, as a wise person once said: (things) are tools and tools break
OH MY GOD I KNOW! I tried to plug in this fudger, a gyro+accelerometer, I think maybe that could have been the thing that fried it, its the last thing I remember plugging in my arduino
It's unlikely that it was the sensor itself. Maybe reversed cables or even trying to connect something with the Uno powered on.