I cant connect to my wireless router in a different room, even with good signal strength?

I have a linksys N router, one of the newer ones (3 months old). I can connect wirelessly in the house pretty much anywhere even if im at the other end where i have 1 or 2 out of 5 bars of signal strength. I sleep in the apartment on the garage, less than 50 feet from the router and i get atleast 3 bars for signal strength, but everytime I try to connect to it it fails to connect. My neighbor on the other hand, who I get maybe 1 or 2 bars of signal strength I can connect to no problems. My neighbor also has only a 3 Mbps connection and I have a 20 Mbps connection. I have tried with the router secured and unsecured. Any suggestions? Thanks and I do give the 10 points!