Mary
There is a date on the bottom in the form of a two digit number set. month 1-12 and then last two of the year. That will at least let you know how old they are. The tank in the picture on top of the grill is an older style tank, just going off the shape and placement of the indentations on it. You need to wonder if the old tank was not working and the guy got a newer tank and another valve steam and tried to get it to work. There a few forum out there just for stoves. Best bet for good advice on just stoves. But...
If you like to just test a few thing first that is easy, getting them to work fully is a different story. first just clean the outsides of the tanks, don’t want dirt to get in there.( I’d start with the newer looking one ). Next check the tanks for rust and dirt inside. rusty ones rattle and rust fall out when turned upside down. If they are really rusty they need to be cleaned. If they don’t look too bad you can test a few more things.
See if the Fuel knob will turn open about 3 or 4 counter clockwise turns and then close back. Check the fuel cap to see if there is a good seal in it. I use the old trick of wetting the cap with a little spit. Next you need to take the pump out. ( do you mind a little bit of dirt or oil on your hands? ) There is a youtube video about taking out the pump and oiling up the leather to make it soft and plyable again. First part of this video is about the pump. It is the same as a stove.
A 2nd life for a dead Coleman pump leatherThis video is about replacing the pump leather if needed( if the leather is falling apart in your hands it is bad). You can also buy a new pump that that has a rubber plunger ( you just swap the old leather plunger one with the new rubber one keeping your old pump steam parts )
How to Fix a Leather Coleman Pump (Replacing the leather)
If you can get air into the tank and it hold pressure you doing fine. Just remember to turn the pump handle ½ turn CCW to unlock the pump steam, Pump about 30 times, keeping your thumb over that little hole in the steam, then push in and turn ½ back until it stops. Now take off the fuel cap, you should hear a “Tank Fart” ( proper coleman technical term) as the pressure is released. If you think the pump is working right ( you can feel a little resistance while pumping ) and you think you got air into the tank but you did not hear the tank fart. take the fuel cap off and place your thumb over the hole. Again pump it and release your thumb. If you now hear the tank fart you need a new seal in that fuel cap. If you can get air in the tank and the pressure holds, you can check for leaks in the sides on the tank by placing it in a bucket of water ( or sink ) and looking for bubbles.
If that worked and it is holding pressure and the tank is not cracked, pump it a few times and open the fuel valve and listen closely to the end of that big long thingy that stick in to the stove for air coming out. That will tell you in the valve is working properly.
Sadly that is about the extent of my knowledge on stoves. Dad never let us light the stove.
Hope this helps.