Ipad 2 A1397, 16 GB WiFi/Verizon: Black/cloudy screen with internet

I've searched the site but might not be smart enough to understand what I'm looking for. Whether I'm using the cell function or WiFi, it'll disconnect from the internet, going to a grayish-black, somewhat mottled screen. Then up comes the normal display within about five to ten seconds. All apps work, and nothing shuts off with apps even when I use them half an hour. Perfect display clarity, color, etc. Touch function works. Fully charged.

Downloaded update to OS via WiFi without any cut-out or shut-down.

What on earth is wrong with this thing? I read the whole process of dismantling an Ipad 2, and while I've never done that before, I'm totally game. However, I just don't know which part I should be replacing. Patient assistance for someone who only understands the guts of a PC is eagerly sought.

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Something happened last night, making it all worse. The touch ability left. It doesn't work with a stylus or finger. Maybe I should re-ask this in a week, just to see if anything else will come up.

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