I would check that you have good connectivity as already stated and if you have a cab you likely have fuses so I would take a look at those as well. The beauty of an old tractor is electrical simplicity, no solid state microchips, just a starter, alternator, battery and lights.
Agreed, although I think of a 2440 as a "modern tractor" rather than an old one. At least it still has simple electrics. When something doesn't start I begin by looking at the battery charge and then at the battery polarity.
If the headlights are bright, the battery is OK. Next is polarity. Make sure that both batteries are hooked together positive to positive and negative to negative. Then I check the ground strap to the frame for polarity. I'm guessing that the JD 2440 is negative ground to the frame. Checking ground polarity is a no brainer for me because our old 2 cylinder is oddball positve ground !! But that is quite the exception. Very few tractors or anything were made with + ground. Remember to Leave the tractor out of gear & key off when messing with the battery. I wear gloves & safety glasses too...if I remember them. Stupid not to use both, sometimes I wonder if I properly appreciate the miracle of good vision.
Anyway, next in the ten minute "farm boy" diagnosis list is always the starter solenoid. Every starter has a starter solenoid and it is usually mounted piggyback right onto the starter. Easiest way to test the solenoid is just to jump between the two heavy lugs on the solenoid with a battery cable. If doing this, be careful not to short the lugs to ground with those big cable clamps. Wear the glasses - if you remembered them... DANGER! Jumping between those lugs bypasses the solenoid entirely and it will probably try to crank. It may even start, although it may need the key on to get the fuel to flow enough to keep running, or it may not. Be careful doing this, some will begin to crank the moment you bypass that solenoid. You are going to be standing in front of the tire while doing this, so BE SURE IT IS OUT OF GEAR !!. Please....
Or you can bypass both key and solenoid by jumping from the battery hot wire directly to the starter itself. That is the common lug between solenoid and starter. If you do, be careful for all the previous reasons. This time it will definitely crank the moment you hit the starter with the hot side voltage. Again, it might both crank and start up the moment you do that. SO BE SURE IT IS OUT OF GEAR.
If none of this makes it crank, replace the starter brushes.
luck, rScotty