Two routers will work out perfect if configured. I use about 5 routers in my old, thick walled, 4 story house to get wireless and ethernet on all floors and area of the house.
Keep your first router setup as is. This get the internet signal, does the DHCP/IP address assigning, etc. Figure out the IP addess of this router, usually 192.168.1.1for linksys default routers.
Get a second router. Plug it directly into a PC into the LAN port without connecting to the other router. This is only to configure it. First thing, setup your wireless info on it for the access point name you want, security, etc.
Now, set a static IP for it. I normally try to go 1 number up from the other router, so 192.168.1.2. Next, disable DHCP on it. We don't want this router handing out IP addresses since the first router will do this and they will conflict if they both try to hand out say 192.168.1.100 NOTE, once you apply these settings, you won't be able to connect with the PC anymore as there is no DHCP so the PC won't get an IP. That's why it's important to set the wireless, apply, set the static ip, apply, then turn off DHCP, and apply.
Now disconnect the router from the PC and plug the ethernet from the first router to one of the LAN ports of the second router and power cycle the router. Give it a minute to boot up. The second router should now connect to the internet from the first one via LAN ports and you can connect to it's wireless.
Now, if this spot in your house doesn't see the first wireless at all, you could give it the same SSID name, so when it looses connection from the basement it will automatically reconnect to the 2nd router as it has the same name.
If you get any signal though from the basement router,then give it a new name as your phone/tablet/laptop will hang on to the basement signal and not automatically switch to the upstairs one.
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