My brother, my advice to you is this:
I have an 04 LeSabre, with some issues, but 132k on the clock. Mostly trouble free, considering I bought it from a "Buy here pay here" kinda place, since my credit sucks. I've had it a year and a half.
I'd go to the owner of the shop and tell him you think he sold you a basket case. The fact that there was rodent droppings under the rear seat tells you they didn't take care of it. Mice only get into cars sitting undriven for a long time. (usually)
Chances are, they chewed into the wiring, and made a mess of the fuse panel in the back. If it really only has 62k on it, it would last you a long time if the current problems are fixed.
I think you have some sort of 30 day warranty on the car that should cover everything. I know when you buy a car in NY, that you get 30 days no matter what, to keep dealers from dumping a basket case on someone and washing their hands of it.
Is it a dealer? Small used car lot? BBB can have some weight here.
Once getting it back, I'd also take it to a good independent mechanic to look it over, for a second opinion.
Sounds a lot like what happened to my sister and her 01 Regal LSE she bought from a dealer. Dealer ended up fixing the problems under the 30 day, (they never really checked the car out, they just got it in as a trade and flipped it). Since my dad had bought 3 cars from them, we went in and let the sales guy have it. They fixed all the current problems, and they gave her an extension to the warranty she bought the car with, out to 36000 miles now, covering everything. Maybe you can get some sort of deal if you push the sales guy.
2004 Buick LeSabre Custom FE5 GXP suspension conversion. 170Kmi
2001 Silverado 4WD 5.3L, 33" BFG ATs, Z71/Z82 pkg, 147kmi.