Hi, and WELCOME TO TECHIMO..!
First off, laptop charge connections aren't the strongest - so if it seems loose, then that could be part of the design... [Trust me, I've just had two laptops become large paperweights when the internals of the power connection broke..!] It is better for it to be easily pulled out than find that the connection/connector inside gets bent/broken - which is what happened to mine.
As you say that one of the chargers is working fine, on both laptops, then it sounds like there is a problem with the other one. As you have two power supply cables, I would (assuming you have two-part cables, like we do in the Land Of Eng) take one part of one and the other part of the other and swap them to check which now works.
If the wall-side half of the currently working one doesn't power the laptop/s when using the currently not working laptop-side half, then the problem is with the laptop-side
part of the one that you said is packed. If it does work, then that pairing is also fine to be kept together, and can be used
If, on the other hand, the wall-side half of the currently not working cable doesn't work with the laptop-side half of the currently working cable doesn't work, then the problem lies with the wall-side part of that pairing.
Of course, this all needs to be done from a known-good socket - to ensure that there is no confusion down to a blown wall point.......
Let us know how you get on...!
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