Hey, what kind of solder are you using? 60/40 or 63/37 rosin core is what you want.
You need to bend the leads around the terminal. I see at least two terminals that are not securely soldered and will not carry the signal to the headphone jack. The jack does not look fried, I would de solder and redo the connections bending the wire and resistors to make a good physical connection and a place for solder to flow into.
I'm using 60/40 solder.
I just tried reflowing the solder and securing the connections, to no avail. FWIW, I don't see any plastic melted on the jack, so I wonder if that is indeed the problem?
I appreciate all of the helpful responses, but I really feel like I'm spinning my wheels here. I don't know what more I can do. I need to walk away from this project for a little while because I'm getting too frustrated.
I built a Fender Champ kit last year, and it went off without a hitch. I thought this was going to be comparatively easy.