manassehkatz provides an excellent answer that covers much of the problems people will face. Some other areas to consider:
The internet is gone. While manassehkatz jokes that teens will die from boredom, the impact is actually far more severe. Much of today's media and knowledge is stored there and is now erased or at best inaccessible. What happens when someone needs to look up a thing, and now that ability is removed? Libraries don't spend near as much money on keeping up-to-date research materials on hand, so vast sums of knowledge are now gone as far as most people are concerned.
Your cars are now useless chunks of metal, plastic, and glass. Without electric spark plugs, no gasoline engine can run. Period. Diesel engines might run, but I guess it depends on how reliant they are on computers nowadays? And of course, even they will require some means to crank, since the battery-powered starter motors are dead.
That last paragraph above just killed entire swaths of your people. Anyone who lives in a city is dead. Period. There are no means to transport goods on a massive scale anymore. This means your city has no food. No food means starvation. You'll have riots before the week ends. And it will be months before order is restored.
Ships at sea will suffer the same fate. Sure, maybe they were at anchor when the surge happened. But now they're dead at sea. All the food being shipped across the oceans is going to rot on board a stranded vessel. I suppose those shipping food can crack open their containers and feed the crew. Otherwise the crew may run out of food before they can reach shore.
Your friendly neighborhood water treatment plant is dead. That's a bad thing. Your water now isn't being pumped from the wells or rivers up to the water towers and out to your citizens. So your citizens are forced to scavenge for whatever water they can find, regardless of how dirty it is.
Your friendly neighborhood sewage treatment plant is dead. That's a bad thing. Now you have raw sewage backing up in pipes, not getting pumped out to the treatment systems or between treatment stages. So the bacteria in them will no longer maintain the balance necessary to survive and treat sewage. This will have long-term impacts for your environment.
Your nuclear power plants are now in melt-down. Sure, they have all kinds of safety measures. But they all rely on various forms of command-and-control systems to maintain them. Those systems are dead, so your reactors are all going to go Fukoshima on you. All of them that weren't already shut down, at least. And there's no way to begin cleanup operations, so the impact will be worse for any such leaks than Fukoshima was/is. (Note, though, that if the world knows these events happen, then it is possible the plants go into a planned shutdown each week during the window. If so, then they're probably okay. Maybe. But it may be impossible to restart the reactors now...)
No one can talk to anyone they aren't nearby. There are no long-range communications methods alive today that aren't electricity-dependent. So we're all in the dark as far as how bad things are at a distance.
No one can manufacture anything. Either because they no lack the means (machines are all dead) or the knowledge (hey, go google how to make a pencil. Oh. Wait. Google is dead...).
Entire industries are dead. Information Technology. Electricians. Electronics / robotics. Publishing. Shipping. Retail. Communications. Entertainment. News. They're all done.
Other power generation facilities may be destroyed as well, or damaged beyond the means to repair without power... Catch-22.
Nations with nuclear arsenals have just lost their control systems. And their electronic defenses. And the electric fences are off for a week. Or more. You've got a high probability that terrorists just walked out with at least some nuclear material from somewhere in the world. If explosions still work, dirty bombs are a high risk and rogue nuclear weapons are a credible risk, too.
Your nuclear subs just sank. If they are in deep seas, then they imploded and probably released radioactive debris, so now your oceans have contamination which is going to cause ecological troubles. I don't know how much nuclear material will be released or how devastating the impact will be, but there's going to be some kind of impact.
Your satellites are space debris. If power restores before they drift off course, control might be regained before they drift too far and eventually are lost. This means no communication, no weather, no spy satellite coverage. It might be a long time before GPS navigation is an option; how good are you at dead reckoning? Of no consequence to the world as a while, but the ISS is full of dead people now and, depending on how stable the orbits are, may be falling or may be at risk of collision with satellites? Either way, there were no survivors on board.
You don't have any factories that are in production, basically. And some of them, if their production lines were running, probably destroyed or damaged their production machines when the power failed without a proper shut down. Food factories now have rotting food stuck in various stages of the line; once power is restored, they'll spend weeks sterilizing and cleaning everything. That means longer delays before food can get to market. Same for medicine factories. Systems that don't have automatic shut off systems (that don't require electricity to operate) may fail. This might impact production lines that involve gas furnaces.
Your dairy farms are in trouble, since they use automated milking systems. A dairy cow that doesn't get milked twice a day, every day, has problems. So you may have collapsed the world's industrial-scale dairy market.
Any farm crops that rely on automated sprinkler systems may have been ruined.
Hopefully, chemical plants, oil refineries, oil well pumps and offshore drilling platforms, etc. all had the foresight to shut down in preparation for the magic day. Otherwise, they may all go boom.
Again, hopefully, no miners were below ground in the mines when it happened. Because they're trapped, have no fresh air coming in, and won't get rescued.
Fire departments, ambulances, and police cannot respond to problems. And, without phones, they don't know where the problems are. So the risk of catastrophic fire has gone up. WAY up.
Ditto if any forest fires break out that threaten towns.
You've lost all your tsunami warning systems throughout the Pacific Ocean's ring of fire. If an earthquake happens, there will be no notice to warn citizens that a tsunami is coming.
Banks and stock markets are down for a week. There's no way to access the funds in those banks. There is no way to verify the funds exist or how much money is held. The entire stock market is zeroed out until power is back. That's a week where the entire global economy just... STOPPED. We see stock markets ripple over things like tweets or speeches. I cannot imagine what kind of insanity would ensue when power is finally restored and trading is allowed to resume.
People would not be able to buy goods since there's no way for them to validate their bank accounts / credit card accounts to withdraw cash. Any attempt to do "old school paper" credit card slips will be horribly inefficient and ripe for abuse. What happens to people with bills that are due during or immediately after the outage? Auto-draft bills wouldn't pay. Electronic payment methods are down. This is global in scale. The economy would take months to correct from this kind of outage. Would there be a run on banks when power was restored? Would the stock market crash as people liquidated their stocks in favor of more tangible assets that can be traded during disasters?
These last two paragraphs alone could trigger the kind of panics that were seen last seen in the US in 1929 when the Great Depression really got started.
You've triggered a Dark Age that will end modern, advanced, civilization.
The Amish are your best hope for survival.
