I dont think I have ever even played on mine besides from some quick testing - I really should spend more time with the systems... With the hinge, normally they go floppy because the plastic cracks, if i remember rightly there is a little "thing" that goes the other side of that metal ring that has a hard clip thing... yea I know terrible explanation but its that that gives the stiffness and the click into place that the hinge does...
I had a good look around last night and your difficulty might be finding replacement shell parts.. I couldn't really find anything for the OG 2ds system.
No worries mate. I scoured AliExpress in the end, have ordered a new screen and plexi. Have managed to find a black top hinge surround which will do, I'll see if I can glue the blue one but if not I have a fall back plan.
Hopefully it's just failing to initialise because of the screen. Would save busting out the hot air.