Is elemental.exe listed in task manager?
What does Properties for elemental.exe say (path, etc.)? Any clues there? My win7 64bit has:
target: "C:\Program Files (x86)\Stardock Games\Elemental\Elemental.exe"
start in: "C:\Program Files (x86)\Stardock Games\Elemental"
run: Normal Window
Have you tried launching with ELLaunch.exe (same location as elemental.exe)?
Do you have any other programs running that may limit available memory/etc.?
Elemental may need to contact SD or some server (it did during beta, I think to ensure files were something or whatever), don't know if that is still the case (I think not) but could there be a firewall possibly interfering? (yes this is a real stretch, but as Sherlock says [paraphrasing] 'when you eliminate the obvious...')