You will probably need to add a wireless access point near the basement computer -- unlikely that any router short of an ASUS RT-AC68U (with the ASUS AC68 pcie adapter or another RT-AC68U in media bridge mode) would cover that distance and those newest routers are quite expensive.
If you can attach an AP with an Ethernet cable or pair of the newest and best powerline adapters (Zyxel PLA5205kit) you will get excellent wireless that should cover the whole house. You can to use any inexpensive N wireless router configured as an AP (DHCP off, different radio channel from main router, same SSID and security type/passkey) and make and LAN to LAN connection with the cable or powerline units. Assign the AP a static address in both it and the main router, inside the network range but outside the main router DHCP assignable range.