Thanks jpm for your suggestion.
I have tried to repair the system with windows cd (via portable usb cd/dvd) but the system didn't see it. Tried with windows usb - there was some progress but ultimately repair failed.
Using the command line after each 'repair' (and I tried over 50 times) I was able to open srtTrail.txt to see what was the problem. Depending on what type of repair was selected (restore pc or repair at start up) the message was either there was one problem but it couldn't be identified, or one or two sys files were damaged or missing from c:\windows\system32\drivers. Upon checking these files were not in the named folder. So I copied corresponding sys files from x:\windows\system32\drivers and were able to progress further, i.e. on the next rebooting (or after several rebootings) another sys file was identified as the reason for the issue and replaced with that from x: drive.
There are more sys files in driver folder on x:\ than on c:\ but I didn't want to copy everything just in case if it makes things worse.
Long story short, this way I finally landed on the message in srtTrail.txt that was permanent with two sys files mentioned there: 1) c:\windows\system32\drivers\drweblwf.sys and 2) c:\TDI.SYS. The first one is a part of DrWeb antivirus, I replaced it using a copy from another laptop (though under different OS- Windows 7) but that didn't affect the message. As for the second one - looks like a registry problem after virus/malware removal like if the system was trying to locate this file on c:\ and since it couldn't do that it wasn't happy to boot up. I tried a little trick of creating a text file in c:\ named as tdi.txt and then renamed it as tdi.sys but that didn't help.
I should mention that when trying to boot in safe more, an autorepair starts but says that the Pc wasn't booted correctly.
I was able to use DrWeb LiveUSB to acess my personal files and run CureIt. Quick scan didn't show any problems but the full scan of c:\ is taking over 34 hours and this is still in progress.
I am able to access registry (via command line or under DrWebLiveUsb) but I do not know how to fix c:\tdi.sys problem. I tried to do a search for it in registry but nothing was found. Neither I know what else to try with regards to drweblwf.sys. Any ideas?
Also I would like to ask if anyone can explain what c:\Recovery\ReAgent.xml does and what it should contain? (mine is currently showing zeros in all id's and path's)
And also what DEFAULT file in config folder is doing? I have made two registry backups just before the system stopped working and have this available in a corresponding folder on c:\. Haven't tried to replace my c:\config with those files in the backup folder as I suspect that the registry there was also corrupted.
I have read
http://www.top-password.com/blog/fix-automatic-startup-repair-loop-in-windows/ and was tempted to try solution 4 but again am scared of making things worse (solutions 1 and 2 didn't solve the problem).
Any help would be really appreciated.