From the sounds of it, the digitizer (the part under the screen that detects touches) stopped working. Could be for any number of reasons. The usual route is to just replace it. You may be able to replace just the digitizer, but in most cases, this is attached to the screen itself, meaning you'd also have to replace that. I don't know what the price of a replacement screen for that tablet is, but if it is as cheap as you say, it might be more affordable to just buy a new tablet.