Does anyone know where you could fix your DS/3DS to a capture card able DS/3DS?

Best place I would say right now is in the Merki.net Discord. While they have retired from producing and selling capture cards they may allow for repairs depending on who made it and what model 3ds you have. Note that the company is based in Germany, so shipping instructions will be very important. https://discord.gg/uM5Bw9UP5x