That shutting down may also be caused by overheating; check the temps in the bios. If it is overheating the processor may get damaged.
I would be keen to discover the cause of the shutdown before purchasing the machine.
It should be easy to change the PSU but there is a chance that the medion has a mobo which is specific to ifself and therefore standard components cannot be used.
My advice would be to get the owner to sort out the problem and then pay a little more with confidence.