Hello.

My RB2011 worked fine around 2 years, but today after I turnet it off and turned on it again - it does not boot.
Only blink by blue Power LED - as you can see on attached images.

Display is turned off and not working any more, ethernet ports has no reaction if I plug cables in it.
Looks like something serious.

Whot it could be? Software or Hardware reason?
Do I need to look for a new router?

Definitely hardware. You have power problems (power supply or some internal components failed) — the BOARD just can't start it booting process.

Does the blue LED sharply blinks or turns on and then fades off?

From what you described I think it could be just power supply (capacitors). Unscrew the casing and try to plug another power supply. Be careful with LCD ribbon cable!
You could also try to power it using passive PoE adapter plugged into 1st ethernet.