Grabbing a signal from next door may be impossible! There is so much between the original router and your basement next door that any signals would be greatly interferred with by the surrounding structures. RF (radio interferrence) plays a huge factor in the signal strength; if you have concrete, bricks, steel, a basement below ground, and any other electronic signal emitters (like an older-model 2.4ghz cordless phone(s) or microwave ovens) anywhere nearby, these will ALL work against you.