Hello,
I am having issues with Legend of Grimrock 1 not starting on my computer. I am playing on Windows Vista 64. The resolution is 1280 X 1024. Sometimes it starts and sometimes it stalls in the loading screen. Is there any solutions for this issue?

It's difficult to suggest anything with so little information to go on. The fact that it starts sometimes and not others (and presumably works normally when it does start) is interesting but doesn't point to a specific problem.

So a few general ones: Are the video drivers up to date? Is everything set to application-controlled / default in the video control panel? Have you tried running it in other resolutions? What about a reinstall?

Hmm, random crashes are indeed harder to debug. At first check GOG's suggestions on crashing.
http://www.gog.com/support/legend_of_grimrock/crashing_in_general

Especially try running the game as an Adminstrator and check if compatibility mode (e.g. for Win XP) makes a difference. Also try disabling anti-virus (go offline before, if you feel unsafe).

If it has the option, try putting your firewall in 'Game Mode', that cured the problems I had.

Overheating? LOG is notorious for frying the GPU, check with GPU-Z the temperature. Also, do you have a multi-monitor setup? LOG is also notorious for doing the initial detection of complex monitor setups wrong; workaround would be here setting the resolution in the grimrock.cfg directly or trying windowed mode.

Hello,
I updated my graphics drivers and it still has issues. I am also playing off of a standard 21 inch monitor. It is frustrating because sometimes it starts and sometimes it stalls. It does not crash, it just hangs in the initial loading screen. I've got an old graphics card, a gt 240. I've read that LOG had issues with starting up. Is 1.3.7 the latest version or was there a newer version I should look for?

Hmmm, try not to move the mouse outside of the window----