Try an app called Wi-Fi Fixer. It's free and might solve the issue. If you need help with it post back and someone will walk you through it.
If that doesn't work,I'm going to ask you some questions you might have already gone through because you're not being very descriptive in what you've already tried.
1) Have you done "forget network" of your home router? If not do that then put it back like when the phone was new. To do that go to phone settings, Wi-Fi , tap the Wi-Fi icon, long press the network at your home, tap forget. Tap home button. Go back to settings, tap Wi-Fi icon, tap add network, if it doesn't show back up on its own, or tap the your home network, tap input your "network key" (aka password).
2) Have you double checked to make sure you put your password into your network exactly correctly? The phone will not give a warning that it's the wrong password, it'll only just not connect.
3) Have you already changed the security on your router while working with anyone at tech support. If so do you know what you changed it to?
4) Have you tried any other secure network, such as at a friends house or work? Best Buy is an open, unsecured network, so basically anything will connect without any effort other than tapping CONNECT.
There are some routers out there, Verizon uses Belkin brand often, that just don't play nice with Android BUT since your Fire is already working fine I am not convinced it's an incompatibility issue yet.
Before you do any of the above steps beyond installing Wi-Fi fixer turn off your mobile network. Settings, mobile network, tap the icon.
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