Forgot to write right away.

The problem solved using Windows Network Diagnostics. After running this tool/app, I was able to connect to Internet from my smartphone. The tool turned out to be a simplest solution. That's all. All the best to netgaters!

P.S. It's is a very strange autoformating of the post... I haven't marked out by another font and haven't used bold face for some text in the main message, here in the thread.