Logitech manufactures wireless mice and keyboard sets. The mouse and keyboard communicate with a single wireless receiver hub that plugs directly into two slots on your computer. The hub receives the wireless signal and sends it to your computer. If there's a problem with your mouse and keyboard or hub, they won't connect and your computer's mouse and keyboard don't respond. A variety of issues could cause your connection problem.
Verify both the wireless mouse and keyboard are turned on by looking for an "On/Off" switch on their undersides and turning them to the "On" position. Some Logitech keyboards and mice lack these switches and are always on.
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Press and release the "Connect" button on the wireless receiver and then press and release the "Connect" button on the bottom of the mouse or keyboard.
Verify both connectors attached to the wireless receiver are plugged into the USB or PS/2 slots on your computer. The connecters could have come loose; try pulling them out and plugging them back in.
Move the wireless reciever hub around. Devices such as speakers, monitors, cell phones and garage door openers can cause radio interference, which interferes with the wireless connection.
Change the batteries on the wireless mouse and keyboard; the batteries may be dead.
Verify the batteries are inserted properly by looking at the diagram inside the mouse or keyboard's battery slot; the batteries must be correctly inserted to power the device.
Move the wireless keyboard and mouse off a metal surface if you're using them on one; metal surfaces can also cause radio interference.
Plug the connectors from the wireless receiver directly into the computer's USB or PS/2 sockets if they're plugged into a USB hub or KVM switch; some USB hubs and KVM switches are not compatible.