Could you post a DXdiag...or at least the drivers for your Intel integrated card?
Intel integrated is good enough to run it, however, if you have DX9, you may have some problems. The Integrated card MIGHT have some problems later in the game I would imagine, as your processor is only a 700 mhz (enough to run the game, but not very well). You said that you had it set to a funky configuration? With Intel Integrated Chips that's not a good thing...AND if it's not a DX problem...could be at the heart of the matter. I would suggest a complete reinstall of the OS with an Update of the bios for your Intel Chip drivers as well...if possible (If I recall, they do update them, however, updating an Integrated chip is a major...you know what).
Next thing to check...once again, referring to the conflicts with your Graphics...make sure there aren't any conflicts in drivers and programs. Do the movies run. Test it out with the Bink Player. If the movies are not running, try running the game with the movies disabled, and see if the game starts up that way.
Good luck. I've run the game on a system almost EXACTLY like the one you are running it on (except it only had 128 RAM at the time). I don't do the internet or use it with the mods or patches though, it has a hard enough time running otherwise. Make sure the screen IS at 16 bit though, just second check that it hasn't reset. I think that would be defined as High Color on the Integrated chips as opposed to True Color which is 24 bit (but I think it is 32 bit on the ATI I'm on right now, checking to make sure and you know what...as opposed to the other machine with ME...this one doesn't let me check the resolution by right clicking on the screen, I actually have to go to properties for that...hmm, I'll have to check that one out, maybe it's something to do with XP that changed from the 98/ME system of doing things).
I have ME on the machine I'm running to, so I think you'll have to have a DXdiag so I can compare and contrast the differences between them (what's different on your system as opposed to the one I have). No guarantees that I can figure it out though, the biggest problem I've had has been slow down in the game on that machine.
I typically play on one of the other machines though, simply because I love playing with the mods (can one say more ships...and even the Constellation Class!).