hi, it looks like those squished/fried lines are the vac lines to the transfer case "motor" . these lines NEED to be the hard, not soft, vac, lines, still available, but you may have to search a little, I know NAPA has 'em, but black only. Eagle has Red/Yellow/Green, the system is pretty bulletproof, IF, both your Vac motors, ie front axle, and transfer case, are functional. I just redid the system on my 84. Takes some time, you need a GOOD diagram, ie , as in the 82 TSM, looks like your front axle lines are ok, but rear ones are fried, so, again, you need a diagram, and some time, and maybe a couple of feet of new HARD vac. line. Congratulations, you are entering the post grad phase of Eagle ownership! Not to scare you, but, rather, to encourage you, The 80s AMC Eagle is one of THE most difficult cars to restore, bar none! This was the "tween" years, the not quite end of carburetion, but not quite full FI yet. Most people choose to discard the whole 80s system, do a ECM Test bypass, and go to a DUI distributor, and/or an MC2100 carb, which I myself have done, with my first one. The second one, my current 84, I did the whole stock/ w/upgrades thing, took over two years, and more reading/research and $$ than I care to remember, but all good now. Point is, don't give up, if you can keep an Eagle roadworthy, you are heads and tails above almost everybody else, with their SBCs, or 5.0s.
good luck, gz