My guess is that the keyboard and mouse are wireless but NOT Bluetooth. Bluetooth is a published, industry standard but most wireless keyboards and mice on the market use a different, non-standard technology than Bluetooth. You may be able to buy a replacement wireless receiver directly from HP.
If the keyboard and mouse support Bluetooth they will most likely have the Bluetooth symbol
on them to indicate that they are Bluetooth.
I'm using a Bluetooth dongle similar to the one that you purchased on this netbook I'm using right now and it works fine with my Targus Bluetooth mouse.