So, your router is in the basement and has an ethernet connection to a PC in the basement, and an ethernet connection to a PC on the first floor....correct?
If you want connectivity to a PC on the second floor the easiest option is to just install a cable from your basement to the second floor. As long as the cable run is less then 100m (maximum distance an ethernet cable can be run without repeaters) you should be fine.
Another option could be to install homeplug adaptors if your buildings main electrical wiring is inter-connected across floors. It would be:
Basement: Router LAN port -> homeplug adaptor in wall socket
2nd floor: wall socket with homeplug adaptor -> PC
Hope this helps.