As lemerise mentioned you have problems with the 2 pins on the bottom left of the socket/connector/header. I will elaborate a little further on the matter. The pin on the end is missing. The next one in isn't soldered to the pad on the board. The socket needs replaced or repaired. It will take someone with above average soldering skills and good optics to replace the socket/header. Repairing the socket/header, judging from the provided pictures, could be more difficult than replacing it. Since this has experienced liquid damage, it is uncertain that either will fix the problem. There could be more problems with components on the board or in the sub-layers of the board. Finding a replacement socket/header should be something that can be accomplished. The majority of the computer/laptop sockets/headers are manufactured by Foxconn, including the ones on Apple products, and are available through a number of sources. You may be better off using an external USB mouse.

Just the trackpad can be replaced. It's Apple part number 922-9063

Personally I had a problem with my trackpad and later found out that directly underneath is my batter. Well my battery was swelling which made it difficult to click down on the pad.