The simplest way to check if it's a fault with the keyboard is to try and borrow one or even buy a dirt-cheap one just for testing purposes. Plug it in and try the <Enter> key.
If there is no problem with that, your BTC6300 is obviously faulty.
You can replace the BTC6300 with any keyboard. Have a look online for something similar.
Open Google Search and type illuminated white keyboard into the search bar and press <Enter>.