The first part of your question was answered, explaining the loss of power due to Red Squad and a rogue part of Star Fleet. The second part is a little tough to answer, but consider the following:
During September 11, 2001, when the World Trade Center Towers were hit and destroyed, what was the initial reaction? That would be fear. We didn't know who did it, why it was done. I remember People talking about possible invasion from a foreign country without any base in fact, only in fear. The entire air travel network was shut down and all planes were grounded. The military was put on full alert. Fighters could bee seen patrolling coastal areas for days after the attacks. Shortly after the towers were hit, we heard reports of the Pentagon being hit. Supposedly, one of the most secure places on Earth, for all intents and purposes, was crippled. Then reports of a fourth plane going down in Pennsylvania, and rumors of possibly a fifth plane that no one could account for. Whether you agree wit US Politics or not, agree with their standing compared to the rest of the world, their influence on the rest of the world, or not, it was the first tie in a long time the US had been so severely hit. The Executive Branch of our Government, the Military and Joint Chiefs of Staff, Emergency workers in all areas directly affected, and the Civilian population were all afraid. Who, what, why, these questions we had no answers to, and because of that, the country was struggling with fear and anxiety. Our entire military, waiting for the order to send them anywhere, some of the best technology in the world at our fingertips, and no where to use it.
Think about it. We as a country, have some of the best trained military in the world, and again, some of the best technology at our disposal, yet we couldn't stop four planes from not only being hijacked within our borders, but being used as flying bombs against a main hub for our military, two buildings dealing with not only domestic, but also foreign trade and economy, and possibly against the seat of power in our country, the White House. We were defenseless that day, anyone that was around and can distinctly remember what it was like, including myself, almost out of high school and ready to join the military, can tell you we were afraid and defenseless.
So how does this relate to Earth of the 24th century? Maybe what they were saying is that the fear of loss of the entire planet's power system puts not only the military, but also the civilians into a state of panic, much like what happened on 9/11. There are varying degrees of defenselessness, one of them can most certainly be paralyzing fear. Any person serving in the military of today, even with all the tech anyone could give them to make war, and train them in the most advanced tactics, is completely and utterly useless if they are completely paralyzed with fear.
Back to DS9. The Founders never needed thousands of Jem Hadar troops on the ground on Earth to make people afraid, but maybe a dozen, two dozen changelings, making themselves visible to people such as Sisko, to let them know they were there and could be anywhere and anyone, could conceivably make Star Fleet turn inward on itself, constantly worrying about who was actually pulling the strings, and in doing so, make the civilians mistrust the military and afraid of them, not knowing who was actually running Star Fleet. The thought process might have been if they can turn the Federation against itself, half the work is already done, and those they would be directly fighting, would be fighting having already been demoralized and paranoid, not only of their superiors but also of each other. If one of the most iconic planets in theFederation were to fall, the allies they were able to amass, the Klingons, the Romulans, and various other races as noted by Picard at the Beginning of Insurrection, quite possibly never would have happened. The Federation would then be fighting a war alone.
Looking at how the entire power grid of a planet being sabotaged might make said planet defenseless, from a logistical standpoint, might not be as grim as it was being stated. Defensive Platforms, Jupiter Station, as well as any other star ships they may have been in the vicinity would have no doubt defended Earth if they did indeed decide to invade at that time. But if any enemy is psychologically broken and afraid before an attack even occurs, that makes the enemy much more willing to either surrender before more lives are lost, or if they don't surrender, will allow for total conquest with less effort.