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You can use the solder points directly from the main chip (the MCU) I've done this kind of work before.Take a look at this work I made.https://www.dropbox.com/s/hzzrzunckfnuctg/reconstruccion%20xbox%20circuito.jpeg?dl=0
Yeah use pin 53 of the SOC board my dude. Hope I helped a fella with this one.
Clean that mess up on the center lead of the Y-axis POT, becasue it sure looks like you have the thing shorted to ground, at a couple of places, which would cause it to act that way.
All there is to B is the contacts, R29 then the SOC board, and the traces that connect everyhting. Not really a great pic to try and diagnose from, but it looks like the carbon contact material (the black stuff) is missing. You'd have to use a conductive pen or rear window defogger repair kit to 'easily' try and fix that.
Nice work so far. You're almost done, please update us when you're done with the conductive glue.
If TP41 is missing then that will also kill the B button. Just prep that via under TP41 and jumper wire from that to the bottom of R29.