Could be many things, we should start with this...
"Try Disk Utility
1. Insert the Mac OS X Install disc, then restart the computer while holding the C key.
2. When your computer finishes starting up from the disc, choose Disk Utility from the Installer menu at the top of the screen. (In Mac OS X 10.4 or later, you must select your language first.)
Important: Do not click Continue in the first screen of the Installer. If you do, you must restart from the disc again to access Disk Utility.
3. Click the First Aid tab.
4. Select your Mac OS X volume.
5. Click Repair. Disk Utility checks and repairs the disk."
Then try a Safe Boot, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.
(Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive.)
At this point, it's a good idea to figure out which eMac variant you have, as some USB 2.0 eMacs have a serious logic board issue that is not practical to repair today. Fortunately you do not have to get the computer running to check which model its serial number reflects.
Use the chart to figure out what variant you have BUT do not post your serial number here.