The main KB is the Logitech one now. A desktop needs only one KB. You can unplug it from the USB port. Keep it handy in case you have trouble with the wireless one. Just plug it back into a USB port.  Manual for the Vostro-- Dell Vostro 270S Setup And Features Information
I had set up the Bluetooth connection of Logitech MK825 Wireless keyboard/mouse combo with my Vostro 270s a couple of months ago. After the setup, clicking a key on a regular wired keyboard won't wake up the PC. Using the Logic wireless keyboard seems to be the only way to wake up the PC.  How to resolve this issue?  
Vostro 270s won't be woken up after clicking a key on keyboard