Can I ask whether you have tried connecting wirelessly when the Ethernet cable has been disconnected.
Your computer specs show that there is indeed an add on NIC fitted in the form of a mini card, your Speccy report however shows that it is not detected and so it has possibly been disabled in the BIOS and may need to be re-enabled, to check this you need to restart the computer and keep tapping one of the following keys to access the BIOS F1, F10, or F11, other possible keys include F2 and Esc, please note that you may need to restart the computer more than once if you do not enter the BIOS at the first attempt.
Once you are in the BIOS you will need to navigate through it until you find the PCI slot information and ensure that they are all enabled and if any wireless device is detected.
From your Speccy report;
PCI Data
Slot PCI
Slot Type PCI
Slot Usage Available
Bus Width 32 bit
Slot Designation PCI1
Characteristics 3.3V, Shared, PME
Slot Number 0
Slot PCI
Slot Type PCI
Slot Usage Available
Data lanes x16
Slot Designation PCI2
Characteristics 3.3V, Shared, PME
Slot Number 1
Slot PCI
Slot Type PCI
Slot Usage Available
Data lanes x1
Slot Designation PCI3
Characteristics 3.3V, Shared, PME
Slot Number 2
Slot PCI
Slot Type PCI
Slot Usage Available
Data lanes x1
Slot Designation PCI4
Characteristics 3.3V, Shared, PME
Slot Number 3
Slot PCI
Slot Type PCI
Slot Usage Available
Data lanes x1
Slot Designation PCI5
Characteristics 3.3V, Shared, PME
Slot Number 4
Please see the attachment below which identifies each slot by number and then refer to the PCI information above and you will note that all PCI slots are listed as Available, this means that the mini card is either disabled, needs to be reseated due to a bad connection or it has failed.