It's fixable.

Toasty. Definitely fixable though.

When in doubt, send it out.

But if you want a project, I'm sure a few of us here will walk you through it.

That is pretty common, and looks way worse than it is. There is not many traces the travel on the same area front and back up there so you can get creative with out it looking like a hack. If there is a room i like to stitch in wires leads from appropriate sized clipped components such as diodes. Looks neater than running jumper wires.

The 2n4401 predriver and 7402 are probably bad after a burned out solenoid like that. Both can be tested with your DMM.

First clean up the burnt areas then re-tin all of those solder points so that you know what you're working with. When pads are burnt, they often are lifted as well, so you'll need to check continuity going to all areas that were burnt to see if you need to put some jumpers in place. As long as you have continuity and the new parts installed also have continuity, you should be good to go. Just keep in mind the boards are double-sided, so continuity has to exist on both sides.