I thought and thought and thought about how to answer that question just using words. I looked for a good diagram of orbital terminology on the Web. Anyway, in the end I pulled out my digital camera and made some toy orbits for you.
An orbit - of a comet, planet, satellite, etc. - is a simple shape, always an ellipse or parabola or hyperbola. (Let's only think about ellipses today. "Closed" orbits are always ellipses.) It takes two parameters, two numbers, to completely describe an ellipse: the "eccentricity" (e) and the "perhelion distance" (d). The eccentricity is basically the "squashed-ness" and the perhelion distance is basically the size. If you tell someone these two numbers, e and d, they can draw exactly the same ellipse every time. I took a piece of cardboard and drew an ellipse with e=0.5, d=two inches. Here's a picture of it:
The "perhelion" is the place where the curve is closes to the focus, or where the orbit is closest to the sun.
That was easy! The reason that orbital mechanics gets complicated is that real orbits don't have to sit flat on the table. They can be tilted and spun around anywhere in space. Of course the sun stays in the same place, so let's stick out model orbit (the cardboard) to a model sun (a ballpoint pen) and see how many ways we can move it around.
So we've got this orbit floating in space. Just for reference, let's say that the Earth's orbit is indeed parallel to the table - that's the ecliptic plane - and that Spring equinox is lined up with the wood grain of the table. (And remember, of course, that the Earth's orbital plane also has to pass through the Sun.) How many different positions can we put the orbit in? We can tilt the whole plane:
(So one of our orbit parameters, the "inclination" (i), tells us where to fix this tilt.) We can also spin the whole thing around the Sun, changing the way it is oriented with respect to the equinox:
(If we specify the "longitude of the ascending node" (w), it tells us where to fix this spin.) There is one more parameter: once we have fixed the plane of the orbit by fixing i and w, we can still move the perhelion around in this plane:
(For some reason, the parameter used to specify this is called the "argument of perhelion", (Omega)).
Does that make some sense? Every frame in those little animations is a whole different orbit, with a different set of parameters. The first animation's frames all have the same w and Omega, but different i. The second animation has a fixed i and Omega, but different w. (This may answer your actual question: if you know the inclination i, you can not figure out the longitude of the ascending node.) The third animation shows a bunch of orbits with the same i and w, but different Omega.
Here is how the numbers are actually defined. Notice that this is the same picture as earlier, but with color commentary. The inclination, i, shown in green, is the angle between the table (the ecliptic) and the cardboard (the orbital plane). Looks like i=30 degrees for this orbit. The "longitude of the ascending node" (in blue) tells you the angle between the wood grain (the Spring equinox) and the "midpoints" of the orbit (where the orbit is at the same height as the Sun). It's hard to tell in this picture, I think that Omega is maybe 45 to 60 degrees. Finally, the "argument of perhelion", shown in purple, is the angle between the orbit's ascending node and the perhelion. The argument of perhelion in for this orbit is probably about 90 degrees.
Given all of the different ways an orbit can be placed in space, all of these five parameters - the shape (eccentricity, perhelion distance) and spatial orientation (inclination, longitude of ascending node, and argument of perhelion) - are INDEPENDENT of each other, they each tell you something different about where the orbit is located. You can't figure out one of them if you know the others. I think your question is, "I know some of the orbit parameters, and I want to calculate the ascending node"? It can't be done; the second animation illustrates how the ascending node can be anywhere, all the way around the ecliptic plane.
I hope this clears things up a bit? Orbital mechanics is VERY hard to think about in your head, or on a flat piece of paper. It doesn't make a darn bit of sense to me until I pick up a toy orbit and spend a while wobbling it around, like in these photos. You might try the same thing at home.
Oh, one more thing: I've shown the "orbits" as fixed loops painted on a piece of paper. In real life, you don't have a big ellipse painted across the Solar System; you just have a lonesome rock which moves along the ellipse. The location of the rock itself at a given time - "where is it today", or "when does it get to perhelion" is one more parameter (the last one, I promise) that you need to know for any orbit problem.
-Ben