Hi Jacob. Tough one but there are a couple things you can try.
You're showing a Standard PS/2 Keyboard above. If it's listed in Device Manager disable it.
Remove the Microsoft mouse/keyboard receiver and try the keyboard with the Advent receiver. You can temporarily use a PS/2 mouse or navigate with the keyboard. Any difference?
Although the Microsoft knowledge based article kb/838398 refers to "response failures in wireless keyboard or mouse" Method 4: Check for interference might shed some insight. Especially note the underlined parts.
Items such as wireless routers, radios, cell phones, desktop fans, fluorescent lights, and large metal objects like computer cases and metal furniture may interfere with the signal of the keyboard. Try to keep such items away from the keyboard, and check the behavior of the keyboard.
Do not put the mouse or the receiver near any electrical devices, especially transmitters such as cordless or cellular telephones or other wireless mouse devices or receivers. A distance of at least 8 to 12 inches is recommended. Do not put the mouse or the receiver on metallic surfaces or objects, especially long metallic rails or cables. We recommend that you keep the mouse and the keyboard a minimum of 3 feet from metallic objects.
It is possible that both receivers are picking up the keyboard signal. That's why I suggested removing the combo receiver. If that is the case you can buy a wireless keyboard/mouse combo very cheap.