Would run for a while (short while), then stop.  Even if the power lasts long enough, which wouldn't be the case (ha, probably wouldn't even last 1 day without humans manning the powerplants), eventually errors will occur, stuff will crash, and everything will fall apart.  And even if it does last that long, all the server/internet contracts will time out, and everything will be locked off.


Almost nothing can last "forever", non-natural and heavy maintenance things like internet even more so.