iPad 1 won't boot, flashes apple logo
Cannot comment yet so I will use the answer box (apologies) - the battery isn't flat if the Apple logo is flashing (requires power to do this). If an iPad has a flat battery for a prolonged period, then refuses to boot when the power cable is in, leave it connected to power for 48 hours+ The batteries on early models are slow to recharge if fully flat, and this is a known recovery process. 

Your actual condition and circumstances (potentially dodgy seller) sounds like they are hardware related, and it could be that someone has opened the iPad to circumvent the Apple ID or replace the battery and made a mess of it. If you are feeling brave my next steps would be to remove the screen (replace with a new one) and replace the battery then check all wiring, solder and connections. The parts are cheap on eBay and the issue might be obvious once the device is opened up.