I am having difficulty launching the game. Whenever I try I don't receive any error messages, and all I see on the screen is my mouse as it would appear at a low resolution. I am running Windows Vista on a notebook. Any suggestions about how to solve the problem or what it might be in the first place?

Have you tried some of the compatibility settings? If you right click on the games shortcut and then go to properties, then the tab called compatibility the settings are there. I would try running as 98/me or xp os compatibility and then disable desktop themes, disable desktop compisition and also make sure to run as administrator.

Unfortunately, despite having tried what you recommended, I still haven't been able to start the game. When I open it, all I get is a black screen with my mouse pointer in the "hourglass" mode.
I'm beginning to question whether or not it might have something to do with my video drivers/settings. However, I don't know enough to make that call.

Do you know what video card/chip and drivers you have installed at the moment?

It's possible you're having trouble loading the intro videos. Try to press ESC several times to skip the videos and see if the main menu loads.

I tried to use the "escape" suggestion, but it didn't work.
The card installed on my notebook nothing special. It's an intel 4 series express chip. It came standard when I bought this notebook. Other games appear to work fine on here. I have played Fallout, Fallout 2, and even Knights of the Old Republic (though hardly under ideal settings). I didn't think a game this old would give me any problems.

Try editing your QuickTime as noted in the Fatal Panic Error thread and see if that clears it up (i.e. maybe it is a "movies" issue).

I tried those suggestions. Unfortunately, They haven't worked. :-\

Could you post your system specs please?

-OS Name Microsoft® Windows Vista™ Home Premium
-Version 6.0.6002 Service Pack 2 Build 6002
-Processor Intel(R) Core(TM)2 Duo CPU T5800 @ 2.00GHz, 2000 Mhz, 2 Core(s), 2 Logical Processor(s)
-Installed Physical Memory (RAM) 4.00 GB
-Total Virtual Memory 7.93 GB
-Available Virtual Memory 5.92 GB
This should be the relevant information. Let me know if you need anything more.
Thanks.

Do you know what graphics card/chip you have?

Ah, I apologize. Here it is.
Name Mobile Intel(R) 4 Series Express Chipset Family
Like I said in a previous post, it's nothing special, but it has run other games for me e.g., Knights of the Old Republic. So, I would expect it to run Septerra Core.

In the compatibility tab is it set to run at 640x480? If not try ticking that, its the games native resolution anyway. If it is ticked try unticking it.

The screen flickered multiple time this time. Otherwise, no difference. :-\

Not sure why its not working your machine should be powerful enough to play this game. If you haven't done so already I would contact gog support and send them a dxdiag.