Yes the real question here is why you can't restart via software. Perhaps a reinstall would help, or maybe it's bad hardware... but the system should be able to restart itself.
Normally when shut down, OS X saves the most recent settings (which windows you have open, any changes you've made in the Finder that it hasn't written) so you can lose these with hard reboots, lots of times after a hard restart a bunch of windows will open that you had already closed. My only concern would be installers that require a follow-up script be run, it may not get activated correctly.