If it's still on the other computer, Amazon's license verification might not be allowing you to run the game. Did you do the licensing from Amazon? I've got a few programs from them, and I can't remember their procedure. It's different from Steam's though...
What I was getting at about the version number of the game, is the actual v1.3, v1.4 or v1.5 (UBoats) of the "SH4.exe" file in the install folder. I don't think Amazon sells a v1.3, which is what the Steam version is, and even if it is, you can at least update Amazon's download. Check that, but it most likely isn't what's keeping you from running.
When you installed the program, did you use what the install gave you, which defaults to C:\ Program Files (x86) \ Ubisoft \ Silent Hunter Wolves of the Pacific ?? If so, you can navigate to the Program Files directory, select the Ubisoft folder, hit <Ctrl><C> to copy it, then go up to the "root" C:\ drive and press <Ctrl><V> to "paste" the Ubisoft folder to C, so that the path now looks like C:\ Ubisoft \ Silent Hunter Wolves of the Pacific (or whatever you have). That will get the game out of the "protected" Windows folder.
Also, when you installed the game, did you let it install the DirectX v9c? You have to do that, even though your computer most likely has a newer version of it. There are a few files in v9 that SH4 is expecting to "see" when it runs, and if it doesn't, the game doesn't run correctly. Usually speaking though, you never get past the menu if it's not installed.
Barring all that, some of the intel onboard graphics cards just do not like certain 3d games. I do not recall which ones do it, but it might be in a post on this site somewhere...
I can't find for sure for certain, but the HD 3000/4000 series seems to be a problem in other games. If that's what you have, you could try what
This Feller Tried, which is a post on the Ubisoft forum for a different game. I have no idea about the efficacy or advisability of doing what he did... YMMV - tread with caution - all them other warnings...