The same thing happened with my hoses, when I looked up under the back I could see the Tee and deteriorated hoses dangling, I am pretty sure being so exposed to the elements helps them deteriorate.
I am pretty sure GM put it back there because it is a bit loud, yours may be in another location, but I am pretty sure it is up under the rear like mine.
If your compressor does not work I'd not bother to replace it, unless you get lucky and find another compressor in a junk yard, they want too much for the compressor at GM, you are better off converting over to gas struts.

you wont be able to get the lines even if you get the compressor, you can get this kit and it plugs in the stock or stock type struts and you can fill them with a compressor, i only have to once or twice a year now. my air below was dry rotted leaking and took out the compressor.

Thanks For that posting Justin. ( I can see u got a little eastern rust there)
My last sedan I also used the Monroe air shocks, & installed the air in valve with a T going to both shocks and kept them at 28 psi. It was easy they did not leak, lasted about 7 years before I needed new shocks & lines again. They work well.

actually the rust on the frame and the important parts are way better than normal, they undercoated it sometime in the 4yrs before i bought it. its very impressive and inspired me to do the same to my 07 monte

On my previous sedan I learned two lessons about undercoating. 1 only get it done in the summer when it is dry and 2 dont use that stinky rubber stuff again. It rained shortly after applying the rubber coating and it got all over the paint, wheels & was unbelievable to remove. Let undercoatings dry for 24 hours before you drive it in the rain. Best to leave it in a warm shop overnight to say the least. Rubber undercoating stinks up the whole vehicle forever it seemed.
SO forget all of that..there are new product that go on like paint, dry quickly,do not reek of noxious fumes, and protect very well. It is a much thinner layer so dont expect the same sound deadening as a rubber layer, but it is worth it.
Platinum shield undercoating $150 is what I recently got applied to my 4x4, while it was new & clean. Lifetime chip or touch ups too. It had a light smell for about 2 days then went away completely, still smells like a new truck today. I had some touch ups done & with salty roads this protection is the best I have ever seen, NO RUST!
Video:

we have the zeibart which is the same it looks like, they warranty it against any corrosion and respray it every year free