HP WLAN turns off when plugged into LAN

This is default behaviour that HP sets in their BIOS.

You need to go into the BIOS, advanced menu, device configuration sub menu and disable the LAN-WLAN switching setting.
Save the setting where you made the change by hitting the F10 key and again when you exit (save settings and exit).
The default is on to conserve battery power (no need to have the wlan card using power when you are connected by wire.)
Of course most of the time you are connected to an ethernet cable, you are also connected to an a/c adapter.

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