I'll try. While I don't doubt the resources aren't the same as they were under the communist system, the main reason for Russia's lack of success internationally over the last two decades is it's now in the same boat as everyone else and most of its officials and fans are in denial.
I think the main reasons were
1. The exodus of the best players who were not available for the national team anymore.
2. The collapse of the level of the national league
3. The collapse of the development system.
Russia produced practically zero talent in the 1990s. Bure, Fedorov, Zubov, Mogilny, Yashin, Kovalev, Gonchar, Kozlov, Zhamnov and Malakhov were the last jewels of the USSR development system. They were all developed in the Soviet Union.
After this generation the next wave of good Russians are the Kovalchuk/Ovechkin/Malkin/Semin generation! Russia practically missed a whole decade of player development, and even the Ovechkin generation cannot be compared to the best Soviet generations (namely the KLM line with Fetisov and Kasatonov).
In the 1990s Russian junior system produced two world class players - Andrei Markov and Pavel Datsyuk. That is only two for a whole decade. It was literally a wasted decade.
The quality of the player development fell so badly that the Russian teams, even those with all the available NHL talent, could not even dream of being as good as those Soviet powerhouses.