My D-pad is stuck in down position

Sounds like you either have something wedges in there, forcing it down OR the rubber membrane between the button and PCB may have been ruined (one way or another). If you have the time and patience, take it apart and inspect that light gray rubber piece. You may end up finding that the membrane has torn a bit. If it's torn, you'll need a replacement part to keep it in the upwards position.

Just give it a good inspection to ensure no debris is in there and that the rubber part is still intact. If those are fine, look over the portion of the PCB that'll deal with the d-pad area and see if anything looks damaged there. Follow this guide to get you on your way. Nintendo 3DS Motherboard Replacement

Update

After the added comment/answer, I did some digging around to find the sticker/metal portion discussed by the poster. I believe this is the item you're talking about, correct? Image of metal buttons attached to PCB. If that is the case, then you'll want to go to the website AliExpress and search for "3DS Direction Key Button Electrostatic Films Set". It's in there, you may need to do a bit more searching if you don't find the linked image right away.

From what you've said with the added information, it sounds like the metal portion has been destroyed and no longer pushing back up. If that's the case, you'll need to order a new one and replace it that way.

I hope this helps solve your problem!