That could be one of a few things, but it is probably a job for a repair shop, but lets try a couple of simple tests first:-
Can this be charged with the battery removed so it's running just on mains ? if so try that.
Do they have access to a similar system ? if so try they're power pack on that system and vice versa, see if the good system can prove if the power pack is OK.
Try gently wiggling the power jack when in the system, don't go crazy, just see if gently moving it up\down etc gets a spark of life from it, if it does then they need a new power connection on the PC, due to the nature of how these connect, over time they can wear, and if this is the case they need to take it to a repair place as it's not a simple job, hope this helps a bit.
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