I'm thinking maybe the wireless card is bad but it shouldn't be because their PC is not that old. My old Compaq that I've had for like way too many years still works perfectly find on wireless and I've dropped it by accident on ground a few times so if my wireless still works their should too. They took really good care of computer and it never has been taken outside so no weather element exposure. I am really baffled if the wireless card is really bad already because the laptop is only a couple of years old.
It seems you have tried everything on the software/driver side, maybe the wireless card is just bad. If you have or know someone that has a wireless USB dongle you could try that it will at least show that you can connect wireless with the PC.
It doesn't appear to be disabled and it is not greyed out just has red "X" next too it. Went to the properties and it doesn't show anything for IP address it has the option selected for "obtain ip address automatically.
I'm not sure if this problem is resolved already. But when you see an "X" next to the Wireless Network Connection icon. That means it is disabled. You have to right-click on it and choose "Enable". Then disable the other one that say "Local Area Connection".
see if there is anyway to trouble shoot the issue, you should be able to right click the wireless adapter then click troubleshoot.
My wireless adapter used to randomly disable itself and the only thing that worked was to trouble shoot it, my system would discover the issue and re enable the adapter, even though I could not manually re enable it myself.