Okay, so your old NAND backup that you restored your 3DS with will not recognize any games and titles that were installed after that NAND image was made. Those games are still in your old
Nintendo 3DS folder.
To get back all your saves, you'll need to set aside a copy of your original setup on desktop. Update to the latest firmware and reinstall fresh copies of all your games.
Now, the next part is going to be tricky.
Back up your freshly installed 2nd copy of the
Nintendo 3DS folder in case this doesn't work out and set this aside on desktop, too.
In the
Nintendo 3DS/<ID0>/<ID0>/title/00040000 directory
, you'll find a list of folders of your games by their Title ID.
For example
The game Pokemon Moon (USA) will be in its folder named
00175E00. Each folder contains a
content and
data subfolders. Your saves are stored in their data folders named as
00000001.sav.
You can try copying and replacing the entire game's
00175E00 folder from the old setup to the new setup. Check if Pokemon Moon appears on HOME Menu. If it shows up, launch that game and see if your game save appears.
If the game doesn't appear on HOME Menu with that attempt, try swapping only the
00000001.sav file.
If Pokemon does show up but launching it leads you to a lost and corrupt save, recopy over that save file again. Use
Checkpoint to make a decrypted backed up version of your save and then restore it.
There are certain titles that have anti-cheating detection that won't recognize your saves if you tamper or change them out. You'll need to use Checkpoint to correct for this.
And again, check if your cards are real with H2testw. Do not assume they are by only judging by exterior labels alone.