Checking dead pixels is easy; all you have to do is check for black dots against pure Red, Blue and Green back grounds. There are few programs you can use to have a clean R/G/B background, but if you have to do it in the shop then you’ll have to use whatever installed in that PC.
The easiest way to do this is by using MS Paint, increase the canvas size to slightly larger than the screen resolution by dragging the corners. Then fill it up with pure Red, Blue and Green Colors one at a time. To choose pure primary colors : double click on any color of the color palette > Define custom colors > Red 255, Green 0, Blue 0 for pure red / red 0, Green 255, Blue 0 for pure Green / Red 0, Green 0, Blue 255 for pure Blue, then look carefully for black dots.
To check for stuck pixels do the same thing with pure Black and White backgrounds.