There's no reason why the router should not give that PC an address. I will assume that the router is OK and that it's DHCP range is more than enough to supply two computer.
However that computer may still be trying to use the same address that was just taken by another computer. You have to make sure that computer can communicate with the router. If the computer can not communicate with the router it will continue to use that IP address until it's lease is expire. If you trying to connect to the router wirelessly, I suggest either disabling any encryption at the moment, disable any filtering you may have and try the following command below or option 2.
ipconfig /release
ipconfig /renew
then ipconfig /all to show us the result
Option 2) Static assigment of IP address, subnet mask, default gateway and DNS. Look into the router dhcp tab. You should notice a range of IP address that the DHCP provide. You just need to pick one that isn't in that range. The only thing you will change differently is the IP address, all other information should look like the other computer.