I have two 3DS motherboards that I'm trying to troubleshoot, so that I can use at least one to replace another that's in a...

I had recently picked up a second hand 3ds a couple of days ago, which was all in working shape (save for a faulty SD card...

Just going to throw this one out here because I had a similar issue with a PS4 (except it would attempt to read the disc for about two minutes, make a loud noise, continue to read, then throw the error). On the bottom of the optical disk drive is a component which contains a web of white plastic gears. It's held to the assembly by three screws. Unscrew these and carefully remove the unit, and at the bottom (near where the disc is inserted into the system) will be a pair of rollers joined by a white plastic piece. In my case, the left roller was not very loose when pressed down on, and would often stick to the plastic. I removed the right roller, and reseated the plastic piece in between and that roller, checking to make sure that both would easily flex up and down when pressed upon. Reassembled everything and just gave it a try, and sure enough my blu ray movies boot right now. The drive is also much quieter now, though I'm trying to deduce the reason to the loud scraping sound that comes during the eject...

If you're turning it on while there's a cartridge in the slot, then it means it's not reading the game, and is acting as if there's nothing inserted (whereas if there's no game inserted, it'll sit at the Game Boy screen since there's nothing to read). Most likely in this case it's just a matter of cleaning the contacts on the Game Boy Advance cartridge, preferably with high-grade rubbing alcohol (I'd recommend nothing lower than 97%). Have you tried staring it up with only one game, or have you tried a few?

I would be concerned that any potential cosmetic fix to the touchscreen would inadvertently affect the performance and accuracy of the touchscreen itself (since toothpaste and other similar products are abrasives, which work by grinding the surface down). I would leave it as it is if it's not causing any issues with gameplay itself, or invest in a screen protector to prevent any further scratches.