Ok, so I tried contacting support, it's been a month, not so much as a "We recieved your support request and will get back to you as soon as possible" so... nice 'work' there guys.

Anyway, I figure I'll repeat my plea here. So I wasted my money getting this, the screenshots got me interested. Anyway, now before the same things get continually repeated... no I don't have UAC on (I'm an IT Technician and a coder, UAC was turned off within 5 minutes of turning my laptop on for the first time...) I have tried all the graphic settings, I've spent hours fiddling with my OWN copy of dosbox, changing a myriad of settings. I've tried and tried, spent FAR too much time trying to get this game working, and all I get is the following:

Click icon, dosbox runs, I get the lil FMV thing for the development company or w/e it is, then where I guess it should go into the main menu or some other video sequence for another developer or something, I get gibberish, pure... utter.. gibberish (See: http://i56.tinypic.com/9lir8p.jpg ) Hell you can even see the contact us thing I had up when I took the screenshot to add to thesupport request.

Well as you can see, after various reinstalls and differing dosbox versions, different settings etc, that is as much as I can get out of the game, and am quite bitterly disappointed in the game (obviously) as hell there's enough topics here of people who can't get it working and have also wasted money, and I'm also disgusted at the customer service (or should I say the lack thereof) of this site.

Guess GoG support are non existant?

I've now sent two, the original one I mention, and one the day before yesterday asking if it's not too much trouble, for some sort of support.

I guess I need to send a 3rd? Should I type "help" in large letters repeatedly to get noticed?

Thanks for that, seems to have worked as they finally mailed me back. Now to see what, if anything can be done, hopefully something either can be done or a refund or something.

I remember having had this problem too, but never fixing it. Seeing this thread made me give it yet another go.
The game does indeed seem to be a bit twitchy when it comes to what it wants you to do and what it doesn't want you to do.
Bit of trial and error later though I think I can supply the following advice which got it working for me:
Step 1. go to the Robinsons requiem folder and make a backup of dosboxrobinsons.conf
Step 2. Open dosboxrobinsons.conf with your favorite text editor, I personally just use notepad for this.
Step 3. Change the output= line to output=surface for some reason I got more issues when trying to use OpenGL
Step 4. Change the line ems=true to ems=false Some old DOS games seem to take offense at you having EMS memory, it seems to run fine without.
Step 5. either delete or alter the line exit to rem exit. I'm not sure how much this helped but it might cause trouble if between the different executions (setup, intro, language, intro 2, menu, game) dosbox executes the next line.
Step 6. Save the config file.
Step 7. (Note I did this for debug purposes and forgot to backup the original), go to properties on the shortcut and remove the "exit" and the -noconsole (or somesuch bit) so you're left with something akin to "C:\Games\GOG.com\Robinson\DOSBOX\dosbox.exe -conf dosboxrobinsons.conf" <---note I've changed the install directory.

Last time I attempted the game it seemed to go further or not depending on whether I was trying to run it in a window, which got me to try to change the output since it shouldn't behave differently windowed or fullscreen unless dosbox handles it differently. With these changes though it seems to be fairly stable. Note it's about midnight here, so no playing overly much on the game to confirm this.

Tried your tips, still I get a lovely screen of gibberish, it's really annoying >_<

Okay I just uninstalled the game and reinstalled it. Running it right "off the disc" it causes gibberish again. Noted that the dosbox shipped with the game is 0.72 while your screenshot is 0.73.
I've run the game through the 0.72 shipped (with altered .conf file) as well as 0.73 and 0.74 generated by D-fend. I'll post that configuration file at the end of this post. It might be something in your default conf file which causes the problem.

Also maybe try to uninstall/reinstall the game. I have a feeling some of the failure might alter the files in the folder.

Also, try to install it in your profile somewhere, like documents or somesuch. I know you've turned off UAC. I've run with UAC turned off, but ended up turning it back on because having it turned off actually broke more things than it fixed. Some programs still don't get the access they need, but are now also prevented from asking you about it. Notable applications I've had that problem with is TIM 3 from gog (which saves in C:\, but would refuse to do so even without UAC enabled), and Steam's beta when they were changing to the new platform. It'd quietly fail, wouldn't tell you why, just wouldn't run. turned out it was running an update installer which required amin access, but didn't get it in spite of UAC turned off. Moving the game folder to somewhere in your own profile should eliminate this problem.

Also, when does this gibberish show up for you? At different attempts I've had it pop up before the silmarils logo animation, during the animation, at the language select streen and even just as I clicked the start button to start the actual game.

As noted earlier, here's my Dosbox.conf file as generated by D-fend, running dosbox 0.73
There's a capture dir a mount dir and a mapper file you might want to poke at.
Also please note that the mount path for some odd reason the mount path is written as 8.3 paths. Not sure if this is important.

# This DOSBox configuration file was automatically created by D-Fend Reloaded.
# Changes made to this file will NOT be transfered to D-Rend Reloaded profiles list.
# D-Fend Reloaded will delete this file from temp directory on program close.

# Config file for profile "Robinson's requiem"

[sdl]
fullscreen=false
fulldouble=false
fullresolution=original
windowresolution=original
output=surface
autolock=true
sensitivity=100
waitonerror=true
usecancodes=true
priority=higher,normal
mapperfile=C:\Users\Drake\D-Fend Reloaded\mapper.txt

[dosbox]
machine=vesa_oldvbe
captures=C:\Users\Drake\D-Fend Reloaded\Capture\Robinsons requiem\
memsize=32

[render]
frameskip=0
aspect=false
scaler=normal2x

[cpu]
core=auto
cputype=auto
cycles=max
cycleup=500
cycledown=20

[mixer]
nosound=false
rate=44100
blocksize=2048
prebuffer=10

[midi]
mpu401=intelligent
mididevice=default
midiconfig=

[sblaster]
sbtype=sb16
sbbase=220
irq=7
dma=1
hdma=5
sbmixer=true
oplmode=auto
oplrate=44100
oplemu=default

[gus]
gus=true
gusrate=22050
gusbase=240
gusirq=5
gusdma=1
ultradir=C:\ULTRASND

[speaker]
pcspeaker=true
pcrate=44100
tandy=auto
tandyrate=44100
disney=true

[dos]
xms=true
ems=false
umb=true
keyboardlayout=US

[joystick]
joysticktype=none
timed=true
autofire=false
swap34=false
buttonwrap=false

[serial]
serial1=dummy
serial2=dummy
serial3=disabled
serial4=disabled

[autoexec]
@echo off
SET PATH=Z:\
keyb US 437
mount C "C:\Games\GOG.com\ROBINS~1\ROBINS~1\"
C:
cd\
cd \
START.EXE start.stp
exit

I had the same problem with the gibberish when I tried it to run on DosBox 0.74 here on my Debian machine, however I just got a black screen when I tried to run it in its native dosbox 0.72 on Windows 7. Then I changed the settings to opengl and to fullscreen=false and it seems to run now.
So you probably need 0.72, as mentioned before.

This is another thread about a game that does not work at all.

GOG you might want to pull this game from the catalog, I suggest everyone start asking for refunds if GOG support is unresponsive and unhelpful.