WOAH WOAH WOAAAAHHHHHHH! I have to
resolder in the shoulder buttons!? I can't solder at all... I seriously think that I just have to relocate the shoulder buttons so it hits the "actual button" shown in the motherboard pics. It CAN'T be that difficult. Once again, I have no soldering experience at ALL.
If only I could show you some of the PMs I got when I tried steering several people into getting a n3DSXL over a n2DSXL... Their defensiveness suggested a disregard or less of a factor that the US $50 (technically $60 if factoring in AC charger) they're saving gets them a system with a less robust and durable design when compared to its 3D siblings.
No matter how careful one will be handling delicate electronics, components will wear down and break within these systems. You just have to be comfortable with that model's repairability limitations when a hardware fault does occur.
As something
@Hayato213 was correct in assessing earlier, this would have been easily fixable if this was a different 3DS model. Except for the o2DS which also has soldered in shoulder push button switches, the o3DS / o3DSXL / n3DS / n3DSXL all have replaceable shoulder button flex cables you can disconnect and swap.
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@Hambrew, I do not suggest fixing those buttons yourself if you do not have experience with the soldering iron. You can easily F-up if you don't know how or have a feel for how melted solder behaves and flows.
You'll need to contact a buddy who's good with the iron and electronic repairs. Offer him some beer money, Chipotle, or whatever small token gift that will satisfy payment for labor.
If you ain't got a friend like that, visit local independent (Apple & Android) phone/tablet/computer electronic repair shops. You'll want to find one that specializes in screen replacements as they have the skillset in disassembling these handhelds. More importantly find a shop that has a soldering workstation on site. Ask if any of the employees will take up contract work with an asking price of no more than $40... That's $10 per each button. You'll have to buy those replacement switches yourself and supply the n2DSXL + switches + payment.
If those prices are not reasonable, you'll have to learn how to solder yourself by practicing a lot with junked and gutted electronics. Look for those irons most popularly sold on Amazon, but make sure you get a kit that has a fine tip adapter. Practice until you no longer fear the scorching heat and strangely enough find soldering an enjoyable hobby.
The last option is to sell yours broken as-is through craigslist. Don't use eBay as you'll get screwed over if the buyer decides to send back a brick, keeping their money and yo n2DSXL. eBay does not provide protection for small time sellers.
The cheapest brand new n3DSXL is the SNES Classic edition for going price of $150 on Amazon, although it's out of stock at the moment after Black Friday. Refurbished n3DSXL from trusted sellers on eBay go for around $120.