My 3DS will not boot. How do I fix this?

My 3DS had a game card in it, then my mom accidentally removed it. She reinserted it after that. Later, when I went to use the 3DS, it showed the message about the game card being removed and how I should press the home button. I pressed it and waited for a while, but the screen remained black. Then, i turned the 3DS off and turned it back on, but the screen was still black. I also pressed the power button again, but just for a few seconds. The menu showed up to let me turn it off, put it in sleep mode, or press the home button. I tried all three options. When I turn it off from that menu and turn it back on, it does not solve the problem. When I put it in and out of sleep mode or press the home button, it shows the white screen with the words "HOME Menu" on the touch screen and it stays there. I have also tried these options combined with removing the game card and removing the SD card, but I have still been without luck. I then tried to call Nintendo customer service, but I was told to send it in for repairs. I also tried reseating the battery and resetting the Wi-Fi card, but it made no difference. After some research online, my dad found the button combination that allows part of the system settings to show up. It allowed me to update the firmware on my 3DS, but after it updated it shut right back off again and had the same problem. My dad also found out that sometimes a problem like this can be caused by a cracked motherboard, so maybe I need to replace that. However, I think I found online that if the whole motherboard is replaced, it also replaces the NAND chip on the 3DS, which would mean that I would lose a lot of data from my software. Plus, because each 3DS uses a different key for encrypting the data and will only read data with the same encryption, that means that I most likely would not be able to use any of the data on my SD card either. Is there anyway I can fix my 3DS without sending it into Nintendo or risking the loss of all my data from the past few years?