No but it isn't a big problem.
I think that having no power is a big problem for an Arduino.
The question is why it doesn't connect to the web?
You didn't tell us anything about your setup, how do you expect us to determine what might have gone wrong on your side? I'd guess it's either because your Arduino doesn't have power (see above) or it's a network problem but you didn't tell us how your network looks like nor did you post your sketch.