My eMachine desk top will not turn off when I go to turn off computer it will shut down but it will start right up again.

Unplug the AC plug, wait 2 minutes, replug the AC plug, and try again.
This is only a first approach to the problem, next moves will depend on the outcome.

There is a virus in your system check for it, there might be a virus in the boot sector of the o.s.

Check for the space available on disk. If too much loaded, del unuseful items