Can't get into recovery / download mode. "No command"

I appreciate the answer! Unfortunately this is among the key combinations I've tried, and the phone fails to respond to it entirely. No idea why as these key combinations seem to work for others with the same problem.

Strange. Unfortunately, it almost seems that its dead. Was it rooted or messed with? If not contact Samsung and see what they have to say. If it was rooted, this is probably the cause and it is probably bricked.

Nope, it was on stock ROM (they're elderly people and have no idea things like rooting even exist). I've tried contacting Samsung but all they tell me is to get it into recovery mode and do a factory reset (yea... Thanks).

Not sure where to go from here. Not quite willing to give up on it just yet.

Im stumped. You could try letting it die and then trying again, although i doubt that will do anything.

Ah yes, I forgot to add that to my list of things tried (though I sped the process up by removing the battery and holding the power button to drain residual energy).

If nothing else works, I might just take it apart and see if there's anything physically weird on the inside. I doubt it... But at this point I really don't know what else to do.