|Sooo What purpose is currently filled by your router if you are connecting to your "ego hungry a-*%&" neighbor's internet (with his consent) ?|
Does your router support bridging or repeater mode? Since you did not give details of the model number we can only guess.
What you need is a wireless repeater positioned as near as possible to the signal source, to boost reception at your PC.
Goin' Fishin' (Some day)