Yes, I've had to think about this one.

I believe it is dissipated (as energy) through the chasis of the computer and into the ground. However, the memory is only as good as that which accesses it, and this is not the same thing. Of course the next thing to ask would be if a computer can become self-aware? This, I can't say.
You believe this to be the case? I may have misunderstood your meaning, and if that is the case then feel free to correct me. However, this is not an accurate description of what happens.
Information in a computer's RAM exists in the form of physical "logic gates". In the RAM, basically it is a series of electrical pathways that are either "open" or "closed" (think basic circuitry, as in a light bulb, a battery, and a switch). All RAM is is a series of these ons and offs. When people say "information is 1's and 0's", what is meant (by the more educated among them) is that information is in the form of either an open circuit (an off) or a closed circuit (an on). At least, in RAM this is the case. In a CD-ROM, pits take the place of circuits. In a magnetic storage device, magnetically charged parts take the place. In a complicated setup of dominos, it is the domino paths. In an aquaduct set up to open or close certain sections based on where the water flows, it is the switches in the aquaducts. I include the last two examples to make it perfectly clear that a computer is nothing more than a series of reactions organized in a special way.
When you cut the power to RAM, all the circuits switch to their default position. Electricity is required to hold them in whatever position they are in. Without it, the data doesn't "dissipate", it vanishes. It is gone, and can't be recovered. The energy involved is in the form of the electricity, but that is not the information itself. The "information" is just the current state the RAM "switches" are in.
Memory is only as good as that which accesses it? How so? A slow processor accessing the RAM may work through the data more slowly, but the data is still just as good. If you mean to say it has to be accessed somehow in order to be useful, this is true. What of it?
And no, the next point isn't simply a question on whether a computer can become self aware.
My point is this. Since the information is little more than the current physical states of the eletrical "gates" in the RAM, then let me ask you this.
If I move a chair, is it's previous position "gone"? That is, does it's previous state exist as a soul in and of itself? Does that previous state of the chair go to heaven? Can it be judged? When it is moved into it's new position, does it gain a brand new soul in the form of it's current position? Data, after all, can be stored in this manner.
I hope I've expressed my point clearly enough.
And now, this idea of "just knowing". There is a fundamental flaw in the idea of "just knowing something to be true". This flaw is how do you know what you "just know" is true? Is it not possible that this "deeper knowledge" you are feeling is an outright lie, or a trick, or perhaps even self delusion? How do you know what you know to be so? I'll tell you this. We "know" not in an absolute sense but in the sense of testing, making observations, and coming up with likely explanations for the sum total observations we have made. The end goal is a full explanation that takes into account every single observation I have made in my life in a way that is self consistant. If an explanation does not tie all this together, it is insufficient as of yet. If an explanation contradicts other parts of itself or previous experience, it is flawed. Many things may contradict. Perhaps you both experience this steady world where you have to eat and sleep and this strange place where you had to give a speech naked and the podium turned into a dragon? So far, the explanation that accounts for BOTH of these observations without making a self contradiction is that there is a real world that is consistant and one part of this real world's rules allows for human minds to enter a "dream state" where imagination is uncontrolled by logic and creates a lot of fantastic imagery. It is the most likely one to be true, and this has been confirmed by observation. We can't just "know" this though. In fact, no matter what you say, you can't just "know" anything. There's no way to find out if what you "just know" is true or not in the absolute sense that you describe. Logic simply doesn't allow for that, and an attempt to posit something outside logic is... illogical

. Even if what you "just know" IS true, that doesn't negate the fact that there is no way you can "know" that what you "know" is "so".
That was a lot to repeat what I started with...