Laptop display panels are tricky.

MAKE SURE you do this when you disassemble.

Take a piece of paper and draw a map of the thing and as you remove screws put the screw on the map to show where it goes. The naked eye is not very good at determining the size of those small metric screws and it is easy to interchange them if you don't do a parts map. I have been fixing computers for years and I still do this with laptops, espeically off brands that I don't see that often.

You will need to pull the lid off, then take apart the frame, watching the little ribbon cable that connects the display to the mother board. That can tear VERY easily. I have torn a few myself. The new screen could possibly cost you more than a new (used) laptop, and after all that you get your old eMachine back. Dell will offer a credit line to almost anybody, and you could get a much better laptop with a warranty and make small payments.

Just hate to see you spend a lot of time on something that won't be all that useful in the long haul.