Reprap RAMPs over heating issues
This really sounds like there is a short somewhere on the RAMPS add-on board. It is advised to not use the RAMPS add-on shield to prevent damage to the Arduino or the shield.

Personally, I would ditch this one and buy a new one. By the looks of the picture you are using a clone RAMPS, these are mass produced and the quality is not always the best (many components are skew). If you are very into electronics you could try to find the short, but it can well be that the traces on the board are somehow connected. Alternatively, you could buy a new board where RAMPS and Arduino are already combined, e.g. an MKS board.