I know of several emachines users who have the same exact problem. Now, I don't mean to insult your machine, so don't take that the wrong way.

The emachine issue has been traced to bad power supplies. We even have an emachine at work here that does the same thing. It runs fine except for the restart instead of shutdown thing. No BIOS settings will fix it or make it work properly, but you can try.
What power supply do you have?