Chosen Solution

Currently my 2.53 GHz logic board has a faulty ram slot. I have cleaned both slots and inserted and removed ram out of the bad one multiple times. Can I upgrade to a better Logic board? If so, what’s my best option?

First try backing the screws that hold the RAM slot mechanism off a quarter of a turn each and test again. Put a 4 GB in the working slot. The one that’s not working will sometimes take a lessor stick. You may be able to use this one, they are both A1278 boards, but I have not seen it listed as compatible. MacBook Pro 13" Unibody (Mid 2010) 2.66 GHz Logic Board

No point really. You could find one on eBay but it is not going to be a big improvement. Can you get the largest sized ram for just 1 slot?

would it be possible to replace the port? someone like luis rossman could possibly replace the port here is his site: https://www.rossmanngroup.com/