Well, I got some tools like my router, bits, etc. and was able to start chipping away at this project (no pun intended).
Since I've never picked up a router in my life and am a general woodworking noob, I have a genuine
fear respect for the tool, so I'm taking things really slow. I was able to route the 1/16" slot for the T-molding and things went perfectly.
I cut the back panel, which will be fixed to the base permanently. I fixed it with about 10 long screws and two "L" brackets for extra support. Drilling pilot holes and counter sinking the flat head screws again went really smoothly as I took my time and practiced on some scrap.
Here's a pic of the base and back panel with the side panel just held up for positioning only. (It's not fixed to anything since it will be cut for a door.) When the base is mounted to the side doors, it will not be flush with the ground. I want about 3/4" off the floor for the base. That explains the gap at the top for now in this pic.
Screen in horizontal mode (there's about 3/4" of free space on each side in horizontal mode):

Screen in vertical mode:

The 19" LCD display I'm using is a Dell 1905FP and it comes with a FANTASTIC stand that is adjustable in all sorts of ways, Up/down, left/right, back/forward, and it locks in rotation from horizontal/vertical. I'd be crazy to ditch the stand so I plan on using it. One thing I have to ensure is that the thing is dead center when rotating. It sure looks that way thus far, but I'll have to do an exact test soon.
In any event, I needed to lock the screen to not rotate from side to side, so this low tech solution should work:

Here's a side pic using some scrap to test the best height/angle fro the display:

Okay, besides the doors needing to open when the LCD rotates, I also have to make the middle marquee light shelf accommodate the turn as well, otherwise the LCD will hit the top of it when it rotates. So I cut a wide slot to allow for the rotation:

Please excuse the poor cutting. It's never seen, but I'll probably clean it up in the finishing stage. I just need a 3/4" finishing bit for the router. After doing this cut out, I'm also glad I went with 3/4" for the extra stability.
Here's a sample pic of the top of the LCD poking through the slot as the LCD turns:

I'll be sure to put the marquee light in FRONT of the monitor slot to reduce any light leakage through that slot and may use a wood partition as well for no light leakage.
That's it for now, next up will be the interior "shell" of 1"x2"s and 2"x2"s to hold up the shelves and allow the side panels to act as doors. Wish me luck.
P.S. QUICK MARQUEE QUESTION: Do people usually use t-molding on the top/bottom? (horizontal, right above/below the marquee art)? How are they mounted? Any link to a specific "how to" on mounting a marquee would be great, for some reason I can't find it. Thanks!