Bitcoin.org offers you different wallets based on user's preferences. This site doesn't have "his" wallet, it showcases different but more or less reputable wallets.
OK, fine, so you chose a HD wallet which uses mnemonic recovery words as wallet backup.
If you downloaded Electrum, then there is no wallet.dat file to be found. Your wallet file has a different name, you can look up its location based on the OS you used (you didn't say about that so far, if I remember correctly). I use Electrum with Linux and wallet files are saved normally in ~/.electrum/wallets directory.
Which version of Electrum do you use?
There is a colored circle in the lower right corner: which color does it show?
Click on the colored circle in the lower right corner and post a screenshot of what you seen in the Network Overview tab.
(You can upload your screenshot to https://talkimg.com/ and insert the [img]link-to-picture[/img] enclosed in [img]-tags.)
If you want to download the most recent version of Electrum, do this only from the official Electrum size which is https://www.electrum.org/ and never forget to verify your downloaded wallet package is genuine (the site provides instructions how to do it properly).