Mark, having solar panels in the sun without a load on them should not damage them. When you use a charge controller, that is what it is doing anytime the battery bank is full, tapering off the load, to zero if need be, to keep the batteries full, not overcharged. I've had mine 14 years, they are constantly being switched off in the afternoon when the battery bank is full. You said 5 year warranty, did you buy them at Harbor Freight? I had one fail a few years ago, and I just called the manufacturer in Phoenix and gave them the serial number on the back of the panel and the volt and amp readings in good sun while the panel was disconnected. They knew it was not functioning properly and how old it was by the serial number, and they sent me a new one. You should not need a reciept for this, unless you bought a cheap set of Chinese panels, this is one of the things that has all the renewable people upset, the flooding of the market with chepa Chinese products. Any Japenese, European or American made panel will have at least a 20 year warranty on them, mine are 25 year warranty panels by Kyocera. Look up the product info on the panel data plate, type it into google and try to find the companies contact info, then give them a call and talk it over.
Having said all that, the burn marks might not interfere with production, you have to unhook each panel, and get a volt and amp reading in good noon time sun, make separate measurments for each panel. Then see if the voltage is near the open circuit voltage (Voc) on the data plate, and if the amperage is near the maximum amp rating (Imax) on the data plate. If they are, the panel is fine. If not, tell the manufacturer what data you are getting and see if they can help. The only point to the reciept is to prove date of purchase, without it, they will just use date of manufacture from the data plate. If you bought them after they sat in the shop for 3 years, then you might wish you had the reciept.
Your inverter is probably junk with the ants living in it. Might have to find a better location for it when you replace it. If the panels are still testing okay, use them. Get them connected to a working charge controller and a battery bank and you'll have 12 volt power to use now. A new inverter can be added later. Take care Mark, Rudydoo