I managed to get access to another laptop to do further research and found a replacement motherboard.
I found it selling here with international shipping: https://www.parts-people.com/index.php?action=item&id=34603
It is listed as part number 9868X
I was able to confirm this was a part used by my laptop by going to dell.com/support and viewing the product specs for my laptop and that part number was listed under: "338-BUXC : Intel(R) 10th Generation Intel (R) Core(TM) i5-10310U vPro, Integrated Intel UHD 620 Graphics, Thunderbolt, 16G" > Part Number: 9868X, Description: PWA,PLN,U,I5-10310U,16G,T,9410