Desktop Hardware and Upgrade Questions

I recently got a new HP Pavilion all-in-one, which came with a wireless mouse and keyboard combo. Right out of the box, they both worked with the PC. There is a USB dongle inside the mouse which I did NOT plug in. I read on a forum that there is an internal adapter in the PC that connects the mouse/keyboard, so, ok. My question is, can I disable it??

For context, when I bought this PC, I made sure to get one with an HDMI IN port, so it could be used as a second monitor with my laptop connected. That works great (with a DisplayPort to HDMI cable) and I'm very happy with it. The problem is, when the laptop is connected to the "monitor," the mouse and keyboard no longer work. They're connected to the PC which I assume is inactive/asleep while the HDMI port is active. But even if I connect the USB dongle from the mouse to the laptop, it doesn't work. In fact, when the laptop and PC aren't connected, and the mouse's USB dongle is inserted in the laptop, they both still only work on the PC. I can't really turn off the PC while the monitor is in use, so simply powering it off to establish the connection elsewhere isn't really an option. 

So, is this mouse/keyboard combo only able to be used on the Pavilion, period? Why did it even come with a dongle? Or can the internal adapter in the PC be disabled, so I can move the dongle freely between devices?