When in doubt, it's much easier to just completely replace the inner tube. They are consumable (like brake pads) and will only cost you a couple of pounds/dollars.
This can be annoying and tricky at first but after a few tries should only take 5-10 minutes or so.
In my opinion, it's easier and quicker to just buy new tubes the next time you're passing a bike shop and spend 15 minutes replacing them than spending several hours identifying and repairing the old tubes - and having the psychological weight of whether or not your repair was fully successful looming over you whenever you ride.
What could have happened ?Not sure if anything in the valve is stuck.
How can I determine what is wrong ?
A number of things. The tyre pressure could have been too high for the weight of the person riding it (you don't always need to inflate a tyre to the max pressure), the inner tube could have naturally weakened with age, the rider may have hit a pothole or thorns/nails without remembering it that pierced the tire and tube.
Ultimately; it doesn't matter. The tube is punctured AND old; get a new one and brush it up as bad luck. I doubt reverse engineering the problem at this stage will help you reduce punctures in the future.