Pure black on a green background means the green subpixel is dead.
Each pixel is made up of three subpixels: Red, Green, Blue. When all are on 100% you get white, when all are off 100% you get black. All else in between creates the various 16.7m colors.
That pink line you are seeing on a white background is probably purple since the green subpixel appears to be dead. The white background probably makes the purple line seem pink.
The only way to fix it is to replace the LCD panel itself which is the most expensive component of a monitor. In your case a new LCD panel will likely cost more than what you purchased the monitor for.