I mean this process: http://wiki.micasaverde.com/index.php/Firmware_Flash_VeraLite. , but the result given by the app was "success".
However, the unit never got working again - leds just blink once after I connect power in, but after that no led at all. The support suggested to try another power unit, but it did not work neither...
The blue power light should be blinking or solid. So like support told you, my first thought is a power issue, which is most likely due to the power adapter since you've already ruled out the wall outlets. Some other things come to mind also:
1) How long did you wait after it was plugged in? It can take 30 mins or so for it to fully "comeback to life" after that firmware flash process. If you haven't already, I suggest you plug it in and let it sit a while, comeback later and see if any lights are on or blinking.
2) I had an issue a while back after a different firmware update that appeared to have bricked my vera. I wasn't able to put the vera in reset mode to load a backup, so I reflashed the firmware (orange zwave light blinking rapidly). Once I got to the step you're at, I couldn't access my vera either. However, it did have the power led on. After some time I then decided to try reset mode again, which then worked for whatever reason. Once in reset mode (blue power led blinking), I was able to access my vera through the IP address and reload my back up. However the firmware wasn't updated, so I went through the update process again and it worked fine that time around. If you think you may be at this point, try putting it in reset mode (blue light blinking) to see if you can access it through the IP address, and if so reload your backup and try the firmware update again.
3) Could be some issue with memory available in your veralite as well, like it wasn't able to install the firmware properly or is corrupt so it just shuts itself off right away. You'll definitely need support's help for that.
Of course, worst case scenario is your vera is dead. Hope that's not the case for you!