Taumauz,
Welcome to the Apple Discussions!
If you're getting no power-on indication at all (no fan, no power LED), try resetting the eMac's switching power supply by removing all peripherals other than the keyboard and mouse, then removing the power cord from the side of the eMac (to remove the trickle current drawn by modern electronics even when nominally off) and waiting 15+ minutes. Then reattach the power cord only and see if the Mac will start.
If that fails to work, reset the Power Management Unit (PMU). The procedure is described in step 6 of
eMac: How to Replace the Backup Battery for nVidia graphics eMacs; for ATI graphics models, the PMU button is on the opposite side of the battery. be careful to press the button once only, firmly, for one second (multiple pressing or pressing for several seconds has been known to permanently crash the PMU, for which the only fix is replacing the logic board).
Note that the first start after a forced shutdown will take significantly longer than usual at the grey screen/Apple logo stage as a faceless version of Disk Utility> Repair Disk runs to check the hard drive for damage caused by the forced shutdown.
BTW, if the computer freezes again, try
command-option-escape first to see if you can force-quit; if not, try
command-control-eject to reboot (see other keyboard shortcuts at
Magical Macintosh Key Sequences).