Not sure I would jump to the conclusion it wasn't well taken care of. It is 5-10 years old and many were fairly fragile to begin with. Also who knows how many people owned it before you. Old electronics are a crapshoot. Even more so video game consoles refurbished by GS. I was tempted to grab one too but glad I didn't. I took good care of my PS3 fat. But after a bunch of years it sounded like a jet. I replaced the heat sync compound and it made no difference. I ended up trading it to Best Buy. It worked fine other then that but perhaps it was on its way out too.
Why do people take such bad care of their stuff? I know the 360 hardware was a little more fragile than other consoles, but the number of busted, dysfunctional systems that are out there now make it actually pretty hard to find a reliable system now.
Hopefully you can exchange it and get a better one.