I want to thank you YOUDAMUSHI one more time. Fixed a problem with Armory in 1 hour.
Extracted private keys from Armory wallet and then created new Electrum wallet importing private keys in there. I got a completely functional wallet. And tested it signing transactions off-line. Works just fine. Fast and smooth.
Finally got an answer from Armory support team:
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It is time consuming to analyze logs to determine why a particular user cannot get their instance of Armory online, so it may be awhile before we can resolve your issue.
We suggest visiting
https://bitcointalk.org........ If you choose to the post your issue there, including your log file will get the best results
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I spent a lot of time trying to set it up the first time. Armory couldn't load a blockchain, needed to download it using Bitcoin Core...
Now I spent about 10 hours of my own time and a week of working computer loading and realoading blockchain and building Armory database, intsalling and reinstalling everything over and over again trying to figure out the problem...
The solution I found is simple - just DON'T USE ARMORY AT ALL