My tab says it's connected to Wi-Fi, but it really isn't?

So, my tab says it's connected to the xfinity Wi-Fi connection, but whenever I try to connect to my Gmail account, it will always say it doesn't have a reliable connection to the server. I don't understand why, as my Dad's phone, my Dad's old phone (Currently mine.), my brother's Samsung Galaxy Tab 3 have Wi-Fi connection. My PC has a internet connection through LAN (A.k.a Ethernet Cable) but the Wi-Fi has the same effect on my PC. No internet connection through Wi-Fi to my PC and tab. I've have tried Factory Data Reset, and still nothing happened. Plus, because of the Wi-Fi crisis, I left my tablet unused and uncharged for 8-11 months, leaving it for dead, and I find it still unable to have a reliable connection. I don't have any other options in mind. I hope someone has the solution to my problem.