Looks like your monitor is dead or the video card is dead. Either way repair will probably cost just as much as a new laptop (unless it is a brand new one, in which case it would be under warranty and would be free to fix).
You can't see it on other monitors because you have to switch the video feed from local (the laptop monitor) to an external monitor. Meaning the video feed would be sent through the 15 pin blue connector on the back instead of through the monitor connected to the laptop.