Let me spell out how to troubleshoot for you:
Is it only the mouse and keyboard that are frozen, or everything? Try for example playing a video and press the reset button and see if the video freezes too. Maybe only USB communication is disturbed, causing the mouse and keyboard to stop working, (if they are connected over USB) but not the whole computer to freeze. Check for this even if the mouse and keyboard are not connected over USB. (Every different thing you try is another data point which may or may not turn out to be relevant.)
Similarly, check that you're not shorting or near shorting +5V to ground when pressing the reset button, for example due to an incorrect pullup, or that the reset pin is connected directly to +5V, either on your board by mistake, or on the wireless transmitter PCB. Again, this may cause the USB rail in the computer to shut off temporarily so the mouse and keyboard stop working. This particular scenario doesn't make much sense since it should freeze the computer regardless of the serial adapter, but check for it anyway.
Otherwise, do the following start with your original setup, with all the wires hooked up. First confirm that you're still getting the freeze. Then try disconnecting one wire at a time and note if the problem stops occurring. Note which wire you removed to make it work. Plug it back in and try the other wires one by one, and also note if any other of the wires can cause the problem to go away. If all that fails try systematically disconnecting two wires at a time etc. 4 wires = 4 bits = 16 combinations in total.
Do you have any application running on the PC side for communicating with the device? If so, does the problem still happen if you're not running this program? If you have task manager open, which does the CPU usage spike when you press the reset button?