
Surely many of those present here use Steam, so I think my story will be here to the point - if not instructive, then at least interesting. Or vice versa.

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I happened to lose access to the account. Active users of this thing will understand the whole horror of the situation and so, I will explain to inactive non-users: the Steam account contains not only games, but also:
- Inventory with coupons, game items, collectible cards, emoticons and other;
- Badges that can be collected from collectible cards, received for contributing to community development or long service;
- Achievements in games that are not always easy to get;
- Access to friends and created communities;
- Library of personal screenshots, illustrations, videos, guides and reviews.
Yes, and some invest in the game more than one thousand money. My situation was not as tough as it could have been - access to the slave account (second, that is, additional) was lost - but still very disappointing! How lost? I did not receive a Steam Guard message when trying to log in from a new device. The login password is correct, the mail is the same - but there is no message. “There is a support service!” - I thought and rushed there.
A couple of days later I received a reply asking to confirm ownership of the account (“Proof of account ownership”). Login-password is not enough for them. To do this, you need to provide some of these data:
- about a credit card;
- on payments by electronic money (AliPay, BoaCompraGold, Giropay, iDEAL, PayPal, PaySafeCard, Russian Kiosk, Sofortüberweisung, WebMoney, Yandex);
- on the Steam Wallet cash certificate;
- about license keys of purchased games.
I sent the data of my credit card, waited for two days - they say the credit card is not attached to the account and even if it made payments on Steam, it does not count. Require another proof. I had no other payment information (QIWI payment data will not suit them), so I sent a CD-key (even two) and waited again ...
Today, after 11 DAYS, the long-awaited answer came:

They closed my ticket until I send them another confirmation of ownership. This time they asked for something completely idiotic: write the number of my ticket as an example with a pen near the license key (yes, right on the booklet out of the box with the disk) and send them a photo.
And this vandalism could go to return the account - but I do not have any boxes, all games are purchased over the network, and the license keys from them look like this:

They prohibit the use of graphic editors, they also prohibit printing. What to do? Nothing. I sent them this very screenshot (only without a blur, of course), but without any hope. You can say goodbye to your account, now for sure.
So, to protect yourself from accidents, be sure to check:
- Whether there is a credit card attached to your Steam account (there, when paying, you need to put a tick "to use these payment data of blah blah blah");
- Do you have access to the email, which made the registration of the account;
- Do you have on hand information about all payments made on Steam (not the receipts that you send to Steam, but documents from payment services);
- Do you have at hand the license keys for all purchased games.
This is the only way to be a little bit sure that access to the account can be restored on occasion. Because, as it turned out, Steam technical support is the one that was still an ambush, and their famous anti-human security measures (which only prohibit the use of the Marketplace in a million different stupid cases) are really aimed at preventing a person from enjoying life.
Good luck to all! Do not repeat the mistakes of others, be original, make new ones.