After disconnecting the ethernet cable from your pc and before you connect it to your laptop are you reseting the router. That may be an issue because though you are connected you have limited or no connectivity on your laptop because the ethernet is looking for the pc when it is connected to the laptop.
I am not familiar with your router but I do know that on mine you have to follow these steps before switching between two devices every time.
1. Unplug the ethernet from the cpu
2. Unplug the power source from the router
3. Press the rest button on the router for about 15 seconds
4. Replug the power source in
5. Make sure that you laptop is off and plug in the ethernet cable
Its hould workout but if not let me know :))