Hmmm... Any time I've used Disk Utility to erase an HD my screen has displayed a "Security Options..." (or some-such) radio button (not a menu bar option) right in the middle of the GUI.
If you don't see the same it's time to ask which version of OS X your eMac discs install; the info won't help me, but it may enable somebody else to help you.
Also, it looks like all eMacs are FireWire enabled, so you should be able to use
FireWire target disk mode to run "Erase" with "Security Options..." from a later version of OS X installed on another Mac. (Be sure your eMac's HD has been ejected from the desktop of the other Mac before you remove the cable.)
Note that one of the "Security Options..." will enable you to sleep better.
Edit: >
Having written that I am wondering if there is any way to check?If you mean check whether your data is still on the eMac's HD, there's no easy way for you to do it, but rest assured that if you only ran a standard "Erase" your data, while now invisible, is
recoverable!