Why can't I log into my Google Account all of a sudden?

I have enjoyed my Samsung Galaxy Tablet 3 Lite up until recently, when, as if out of nowhere, my device decided that I was unworthy of the Google Play Store. I searched far and wide on the internet and have found various solutions, none of which have worked (I will admit, however, that I may simply be too much of a moron to do them correctly), which has brought me to factory reset my device. This seemed like a good idea at the time, and even slightly after when my device powered on after the reset, but when I was given the choice of logging into my Google account (Given the choice between "Existing" and "New") I am able to select the "Existing" button and enter my information, but when I attempt to act further a screen appears "Signing In" and then shortly after is replaced by "Couldn't sign in; Can't establish a reliable connection to the server. This could be a temporary problem. Try again or connect to another Wi-Fi network." and then, upon clicking "Next" it takes me back to the screen to select my wifi network and the process repeats endlessly. I initially thought that it was just bad timing, and so I tried continuously for longer than I'd like to admit with different networks and accounts, but nothing ever changed, and now I am here honestly disappointed that my marvelous device has become utterly useless due to an issue I don't even know. Please help.

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