Definitly something amiss here. You should have no problems. I'm running Windows 7 64bit without difficulty. A word of advice. Read the suggested "Windows 7/Vista" install procedure, and follow it to the letter. Create a folder on your C drive, and install the game there. Be sure to run and install as administrator. Make sure youre game shortcut is not pointing to SH4 GUI. Make sure it's SH4 EXE. Your hardware seems up to the task, so I'm thinking it's a software conflict. Sorry I can't be of more help. Good luck! Here's the install info:
http://www.subsim.com/radioroom/showthread.php?t=150997