broke off the connector for power supply

I recently got a used DSi XL untested. When I plugged it in, the yellow charging light blinked, and it did not power on (occasionally an attempt to power it on would result in the blue light turning on for a split second, but most attempts to turn it on resulted in nothing). I cleaned the battery compartment with 91% isopropyl alcohol. I tested the battery and it seemed to be working. After reseating the battery in the cleaned compartment, I still had the same problem… so I unscrewed the back and took it off (careful not to tear any of the ribbon cables). If anyone knows a fix to this issue, thats also welcome, but as of right now nothing is going to work because I also broke the connection of the power supply (which is my main question):

unfortunately when I was removing the circuit board under the battery compartment, I misunderstood the instructions and removed the entire white square with the + and - (red/black) wires (as opposed to removing the piece within the white square). I was wondering if I should solder it back on (and if so, what tools are needed for smthn so small) or if there are other possible solutions to reconnect the supply current (like maybe just securing the piece exactly so with electrical tape? would that be enough to complete the connection?).

I broke off the piece that connects the battery to the motherboard and dont know how to reattach it/if reattachment is possible.

thabks in advance to any answers!