I wrote everything above about citizenship.
Still that can't stop you from getting a passport, which would be a form of identification they accept.
But anyway, if you can't provide another form of ID that's you problem actually, as Coin_trader has stated.
By the way, there is a way to obtain citizenship, Wikipedia states:
Quote
After independence in 1991, the Estonian government granted Estonian citizenship to the persons who resided in the country before its annexation by the Soviet Union in 1940, as well as to their descendants. Those who could not prove that or arrived after 1940 and their children born in Estonia or elsewhere could acquire Estonian citizenship on condition that they be proficient in the Estonian language and know the country's history. But about 125,000 people (most but not all of whom were Russian speakers) who failed the tests or refused to take them have become stateless, or “non-citizens”, who hold a grey passport. Tens of thousands have opted for the red Russian passports proposed by Moscow. After a change in the law in 1995, all children born in Estonia after 1992 may obtain Estonian citizenship subject to certain conditions.[1]
If you live there for at least 32 years you should speak the language and know some of the history I suppose.
I can get a passport, it costs 45 euros, are BC.game ready to pay the cost of the fee?
It's only been online for 4 days, so far everything's ok 
.