There are quite a few theories that come to my mind right now, none that is easily diagonosable.
Start setting: bluetooth dongle, wireless keyboard and mouse. You don't specify if the wireless kit receiver connects via PS/2 or USB, nor if the receiver is RF or IR.
Status: doesn't work after bluetooth dongle starts
End setting: bluetooth dongle removed, keyboard and mouse replaced with wire versions.
Middle setting that you didn't do: bluetooth dongle removed, wireless keyboard and mouse attached.
Status: yet to find out
My theory nr. 1: if the wireless kit uses RF to communicate, it could be interfering with the bluetooth dongle, thus none will work because they can't talk to anything. If it uses IR, RF interference is not possible and this theory fails.
I have no theory nr. 2 right now.
Can you please try the "Middle setting" I described above and see how it behaves? Thanks.