Hello, I bought the square enix bundle which is just a repackaging of the gog releases. I tried running the game from the shortcut (it uses dosbox automatically) and it gave me a blue screen.

OS: Windows Vista Home Premium fully updated
My laptop is a Sony Vaio VGNAR71M with the following specs:
CPU: Intel Core 2 Duo T8100 2.1GHz
GPU: Nvidia GeForce 8400M GT (Driver version : 7.15.11.6760) (latest) 256MB
RAM: 4 GB DDR2
No firewalls, no anti-virus programs installed

As it blue screens, I can't really find any crash reports on it. Where do you think a report should be? I can't find a crash report on the tomb raider directory.
Thanks in advance.

Try this - http://www.nirsoft.net/utils/blue_screen_view.html

I have no clue what this is. Any ideas?

Dunno, not an expert on BSOD, but you can look here or just google for more results. ;)

https://answers.microsoft.com/en-us/windows/forum/windows_vista-system/bsod-caused-by-ntkrnlpaexe/a37f0b5d-c3e6-41a6-8d5b-7a84384f8820
https://answers.microsoft.com/en-us/windows/forum/windows_vista-performance/win32ksys-blue-screen-crash-on-vista/c81befb1-07d4-4863-8852-fc84cd622937

I think it's now worth trying this installer version I just posted
@ tombraiderforums.com
in the "tomb raider" section of the forums
the thread called: New version of my TR1/UB dosbox installer
on page 39
see post #389 for the link
which ought be perfectly gog-compliant

the mate who tested it reported it worked for him

I already posted a solution for this - http://www.gog.com/forum/tomb_raider_series/does_this_game_work_with_a_controller

I had tried that and blue screen occured for the first time :/

The microsoft forums did try to help, but with no results. I'll try to run it directly.
EDIT: Running it directly worked!
Here is how I did it:

#1
I used the GOG image file (game.gog) copied it to a simple directory I made with no spaces (e.g. C:\dosgames/tr1)
Then I renamed it to .ISO and also copied the other files in the TOMBRAID folder (the exe etc) and mounted the whole folder on dosbox directly. (just drag and drop the folder to your dosbox shortcut and it will do it itself)

#2 Proceeded to mount the image file (I named it TR1.ISO) with the command imgmount d "x:\path\TR1.iso" -t iso
#3 Now that the image file is fully loaded on dosbox, all you have to do is type the name of the .exe, i.e. type "tomb.exe"
#4 Play the game.

Please mark this as solved :)