I can only guess, but to me it sounds like the magnetic sensor that indicates your lid is closed is damaged. It goes into sleep but if your monitor is plugged in, nothing happens (as expected). Problem is that the resistor is on the logic board. It is going to be expansive if you do not know much about soldering and that stuff :-/
A workaround would be to go to settings and change the option when the lid is closed to do nothing