I'm gonna guess its the same POS HP tablet pc I have (with the same problems). The generic model is a HP Pavilion tx1000 and there were many variations of that model, mine was a tx1220us for example.
If you're willing to take it apart and fix, the problem is the heatsink is not actually in contact with the GPU with a penny sized gap between it. It's a design flaw that HP won't acknowledge and a well known problem. The GPU gets so hot that it lifts off its seat and thats why the screen goes out. A sign of it going bad is losing the wifi, this means you have 2 months before the screen goes out.
You can fix it if you get a heat gun(quick) or blow dryer(long) and heat up the GPU so you can reseat it back in place by pressing it down with a towel because it will be very hot and holding it down until it cools. Then putting thermal compound on both sides of a penny and put it on top of the GPU followed by the heatsink. You can google "tx1000 penny" for more complete instructions.
Its a temporary fix and won't guarantee the screen won't go out again but at least you know there is a fix when it does happen again. I know its annoying, I have one I barely use anymore. It sits there as my last resort computer of use and out in the open in plain view in case anyone breaks into my apartment they will be satisfied stealing that instead of my other stuff.
If you salvage parts from it, you can probably use the ram, dvd drive, wifi, and hdd in a small form factor (mini-ITX) HTPC build, maybe even the CPU may be salvageable. maybe the bluetooth too since its on its own chip, but I'm not completely sure how to connect it to something else. Aside from that, you can probably sell the battery to someone else with this POS laptop and maybe the rest of it for "parts" like the screen if they happen to break it before the screen goes out.