When I get to the gameplay, the cursor is not seen and it looks like it's flickering?

what game are you referring to overseer or something else. If it's overseer - is this version 2 installer dvd version.
the flickering could be your driver as overseer at times does not work with the latest video drivers especially the nvidea ones.

start with editing the tex.ini file to make sure lock video is set to "1" & not "-1" this usually helps with a mouse .
don't run dual video cards also.

you may have change your graphics driver, I had a problem with my driver at one time & the whole screen had lines all over it & once I went back to a previous version it fixed the issue. I think from memory I used my on board graphics rather than the nvidia driver to over come this problem.

oh because that's the problem that I have, the intro/part where you talk to chelsee plays fine but when I get to tex's office, the cursor starts freaking out

now is the change to a previous version something I do on my graphics drivers properties or from the options menu in the game

what graphics card do you have & what driver are you using as I have the same thing happening if I use the nvidia driver
when I change to onboard graphics this flickering goes away. If you don't know these details go to control panel in windows & under system look in device manager & click on display adaptors .

is this the flickering you are getting
https://dl.dropboxusercontent.com/u/21372568/VID-20140109-00000.3gp

I have found a way to fix the graphics problem on windows 8, there is a program that i have found called 3dripperdx which allows me to play without any graphical problems so if you want to play it on windows 8 then this is the program to get

http://www.deep-shadows.com/hax/3DRipperDX.htm

Sorry to bump this old thread, but I'm playing Overseer now, got the midi working (with VirtualMidiSynth), got the movies working with the updated ffdshow, and got the textures OK with the dgVoodoo drivers.

Only thing still bothering me is this flickering (arrow) cursor. The ingame crosshair cursor is fine. When it turns into an arrow it dissapears and only appears when I move the mouse. Very irritating!

You said: "when I change to onboard graphics". Where exactly do you do this?

-- EDIT --

I noticed that when you change the ingame resolution to 480 * 640 instead of 600 * 800, the flickering / disappearing of the arrow cursor is gone... It does not change a lot to the game. game windows will be just full screen and the menu will be bugger (so will look a bit less "high res"). But I prefer this 480*640 view with a "stable" mouse cursor, to be honest.

Going through Overseer now, and I have a similar issue with flickering cursor. For me, if LockVideo in the Tex.ini file is set to zero, it flickers anywhere on the screen while in-game. If it's set to 1, it looks fine from the bottom of the screen to about where 480 pixels in height would be, but anything above that and the cursor begins to flicker. So it's a coin toss whether I play the game at 640x480 or live with flickering on the top 1/4th of the screen, but I'm going to keep looking into this and see if there isn't some fix.
Edit: Running 640x480 causes now half the screen to have a flickering cursor. Setting the resolution to match my desktop in dgVoodoo2 causes the mouse to appear on the entire screen, but rapidly flickers.
Edit 2: Using RivaTuner and capping the frame rate to 120 caused the flickering to be a much less frequent concern, and lets the game still run smoothly. Probably if I didn't have an integrated Intel GPU and had access to a graphics card app with vsync and frame capping options, it wouldn't have been this much trouble.

For flickering cursor you can try disabling Windows GPU Scheduling (called hardware acceleration on older Windows). I've found that fixes that in a different game. Its a possibility. That other game might also have needed some compat settings to fully fix stop it, but I can't remember now.

However, I would fully expect a ddraw project to fix it as it works around driver and other issues. This would probably be the better way to go. The one I recommend is https://github.com/narzoul/DDrawCompat/releases and just download the one zip, extract and put the ddraw file in the game folder, start the game, and see if blinking or not.. Overseer works great with this. I have more info on it in another thread: https://www.gog.com/forum/tex_murphy_series/graphics_are_terrible_and_overseer_keeps_quitting/post19

Indeed, in the end the DDraw fix from this link ended up working best for Overseer, most of my issues are resolved. DGVoodoo causes problems with the mouse cursor during the brain implant puzzle, making it virtually impossible to handle the mouse.