When you go to "Device Manager' and look under "Network Adapters", is the Intel(R) 82567LM Gigabit network Connection the only adapter you see on the list?
Intel(R) 82567LM Gigabit network Connection is not capable of connecting "Wirelessly", as this interface has an RJ45 port for cable.
If so, this can indicate that the "Lenovo ThinkCentre" would only have a wired connection, not a wireless device that can pickup the broadcasted signals from the router. The only way you would get internet connectivity would be using the wired connection directly to the modem or router.
Hope this helps,