I have a battery charger that uses a 24VDC 300mA wall transformer. The transformer died, and the closest replacement I could find was 24VDC @500 mA. The new transformer did seem to charge the battery pack just fine, but the next morning it too was dead. Is it possible that the higher amp rating caused it to burn out? Or should I rather suspect that the battery charging circuitry has become defective?
No, the higher amp rating would just mean it can supply more current if the circuit "asks" for it. The voltage rating is the main thing here, and that matches okay.
The fact that the 500mA power pack blew too suggests something is pretty wrong somewhere. How did you confirm it blew? Have you tested the output with a multimeter?
What model charger is it? Are the batteries you are using the correct type for the charger?
If you have a bench supply you could plug it (current limit it to say 400mA) in and see how much current it is drawing. I would test both with no batteries in and batteries on charge.
If you don't have a bench supply with current display you could rig a 24V source up and use a multimeter to test current.
Also, other clues you can check for - see if any components are getting very hot (especially if not loaded with batteries) With circuit off, test resistance between power and ground to see if it is low. I would be suspicious of anything under 1k or so.
You say "transformer", but a transformer doesn't put out DC. The wall wart must be more than just a transformer.
The current rating of a power supply only indicate what it can deliver. The load decides how much to actually draw. A 24V 500mA power supply is therefore a superset of a 24V 300mA power supply. Unless the power supply has deliberate current limiting and the particular load makes use of that, there will be no harm using the 500mA supply instead of the 300mA supply.
It sounds like the original was just a ordinary off the shelf power supply, so most likely did not have particularly accurate or specific current limiting such that the load could rely on it. That would be unlikely design anyway. Therefore, no, most likely no harm was done using the 500mA supply.
It is strange that this supply also died. These supplies are usually short-circuit protected. Even if the load were a dead short, they therefore should not be damaged. However, there are a lot of cheap supplies optimized mostly for low cost out there. Some even outright lie and don't do what the nameplate says, or only in the best possible conditions you're not likely to duplicate.
Does the new supply have a fuse? If so, the load could have a short and the fuse blew like it should. In that case, replace the fuse and the supply will be fine again, but the charger is dead.
Test the new supply with a meter without the charger connected. Is it really dead, or just act dead with the (probably broken) charger connected?