black screen at the start of the 3ds

Does your 3ds have cfw? Such as Luma cfw?

 

1. Do you have B9S and Luma3DS installed?
2. What happens when you power on the system while holding down the Select button?
3. What happens when you boot the 3DS without the SD card?

 

What do you mean you "recovered an old 3ds"? Did you get it second-hand? Are you sure it was never hacked in any way? What happens when you try to update in recovery mode?

Assuming it's a software problem, I'd recommend using ntrboot to install B9S and perform a CTRTransfer. That should fix the problem.

 

For o3DS, o2DS (early model), and o3DXL, reseat the WiFi module. If it comes off or becomes loose, it can cause black screens boot.

• [iFixit] Nintendo 3DS Wi-Fi Board Replacement

 

Does WiFi work in Recovery Mode?

 

Go with Lacius advice. Hack the o3DS with custom firmware (ntrboot / ds flashcrt) and repair the 3DS firmware with CTRTransfer.

If that doesn't fix the problem, you might have a variety of this particular Black Screens of Death.

• New 3DS XL Screens only display recovery mode

 

See the ntrboot capable flashcarts list; only models on that list work. *Except for R4i Gold 3DS Plus and Ace3DS X, requires another (o/n)(2/3)DS(i)(XL/lite/phat) to reflash the cart in ntrboot mode.

 

If the label does not state "www.r4iultra.com", it won't work. Too many R4(i) clones look like one another. Reflashing ntrboot on noncompatible flashcart will brick it.

ntrboot options:

• R4i Gold 3DS Plus (www.r4ids.cn) [highly recommended; has dual mode switch]
• R4iSHDC series (www.r4isdhc.com) [cheap but has shitty time bomb. requires reflash].

 

That's the highest open firmware that a nonhacked 3DS can be when flashing ntrboot to that flashcart due to the Nintendo DS whitelist block. If yours (not your friend's) 3DS is already hacked, you can flash ntrboot using Flashing ntrboot (3DS Multi System) [French].

Edit - If not hacked, first hack yours with [frog/fred/steel/seed]miner, then reflash ntrboot on the cart once hacked, and finally hack your friend's 3DS followed by CTRTransfer.

 

If you have a 2DS or 3DS that already has boot9strap/GodMode9/Luma3DS, you can put your flashcart made by (www.r4iultra.com) into ntrboot mode using the ntrboot_flasher FIRM payload. A hacked system is not restricted in converting an (ntrboot compatible) DS flashcart.

The 4.3.0 or lower open firmware only applies to nonhacked 2DS/3DS as their DS(i) mode will prevent older DS flashcarts from launching at HOME Menu (cannot access the ds_ntrboot_flasher *.nds app).

If your 3DS system (the working one), is not hacked and is at 11.10.0-43E firmware, you must either resort to hacking with seedminer method, get a different ntrboot flashcart (not blocked by the DS cart whitelist), or find someone else with a hacked 2DS/3DS who flash ntrboot onto your R4i Gold.

 

English lexicon clarifiication
cracked = hacked
linker = flashcart

Yes, it will work. Remember, only flashcarts found in that list [see image #1 and image #2 *].

* The diagram in Image #2 is a bit outdated as certain models made by www.r4isdhc.com were supported with ntrboot later.