Samsung Galaxy S5 — network problems

My Internet cable connects through a modem to a very good router that connects by Cat5 cable to a new Netgear router acting as an Access Point inside my residence. That works great for various notebooks and DVD Players that access the WWW by WIFI inside the house. It worked fine on my Nokia cell phone and my wife’s cell phone. Every device uses the same settings and same password. Instantly works.

But when my brother was here over the Christmas holiday, his Galaxy S6 would NOT login to the Access Point signal. I just changed to a Galaxy S5 and am experiencing the same problem. My Galaxy S5 phone sees the Access Point signal very strong, but like my brother’s S6 it will NOT login. I have checked all the settings a dozen times. He and I are inputting the correct password. When we try, our phones briefly flash “incorrect password.” So obviously the fault is the two Galaxy phones. What are we doing wrong?