Once you have everything gathered, we'll start with the basic frame. By the end of this step, you'll have something that can stand up and look like the skeleton of the cabinet.
Using the design you did earlier, trace a cut-out template on a piece of thin plywood or the like. You'll need to measure out the lengths and angles you can easily do from either end, using the square to measure the verticals and horizontals before drawing out the diagonal lines, and then making sure it all meets in the middle. Go over this several times to make sure it all looks just right before you cut, and then cut with the jigsaw very carefully.
Once you have the template perfect, use your table or circular saw to cut the rectangles of the two side pieces. Whichever two edges are original edges should be the bottom and front, since they'll be guaranteed to be straight and at right angles.
Then clamp the template on and trace it with a sharpie, and jigsaw-cut out the matching piece -- if you're not sure about your cutting, err on the side of cutting too little. Once you've done both sides, lay them atop one another and look for any disparity, and if you see any, trim them to match with the jigsaw or sander.
Measure up the edges and make sure everything's about where it should be, and make any more trims necessary (being sure that they match on both parts) until it is. If the line where the speaker plate will go is too small, that's probably no big deal, but if the monitor line isn't big enough for the monitor, you have to adjust that now.
At this point, sand the edges. Where there are sharp corners, but less than ninety degrees, sand them well to make them rounded, so the T-molding can go on easier later (and to give the case a nicer look). Everywhere else, just get those edges smooth, and keep the sheathing of the melamine from breaking or peeling.
Next, cut the base and top pieces, plus the thin strip that will be the middle of the back (the bulk of the back will be the two doors). As these will all be the same width you'll probably cut one piece to that width and then cut off slices for each part. (Quite a few other pieces will be that width, too.) Give their edges a good sanding too (generally, you'll sand every edge you cut to keep from having sharp edges and to keep the melamine sheathing from breaking or splintering).
Before doing anything else, mount the feet on the base. It'll be so much easier to do now than later. You will have to fiddle around the feet somewhat as you move the case, but it's worth it.
Stand the sides up on their backs and position the base, so the entire frame looks like the case lying on its back. Use corner clamps to secure the base into place against the sides. Drill pilot holes, then use the Dremel to carve out a conical hole around each one for the head of the woodscrew to sit flush in, and finally screw them in. Add more strength to these joins with L-brackets inside the case.
The top plate also needs a lot of preparation before it can be screwed in the same way. First, position the fluorescent light and vent fan on it, making sure there's enough room for them both, plus room for the groove for the marquee, and the back door too. Trace the vent fan's circular profile and then cut out a hole using a drill and the jigsaw, then screw the fan and light into place.
On the other side of the vent fan hole, either affix the grille, if you have one, or if not, make your own by cutting out a square of screening material, folding over the edges, and then screwing that down. Since this will be on the very top of the cabinet, it doesn't need to be pretty, it just needs to keep flies from getting into the cabinet and provide some protection for errant fingertips.
If you have a router, you'll know how to use it to cut a groove in the front of the top for the marquee. I used a Dremel by clamping down a straightedge (my level), then cutting along it with a disc to make a thin line, then removing the level. I then deepened the cut a bit before applying a broader stone tip to widen the groove. I made it about 2mm deep and approximately even all the way along; it doesn't have to be too precise, though it does have to be straight.
Once the top is all finished, affix it just like you did the base (probably will only need one pair of brackets... and there will probably only be room for one pair). Then you can stand the case up and finally screw in the back brace piece, which will give the case enough stability to be moved around (carefully).