HayleyAJay,
Welcome to the Apple Discussions!
What model (CPU speed) emac do you have? (You can add useful information such as your Mac model, OS version, CPU speed, amount of RAM, notable peripherals, etc. using the My Settings link in the box on the right of the Discussions pages.)
If you have a 1.0 GHz model eMac, check it's
serial number against those covered by the
eMac Repair Extension Program for Video and Power Issues (rndom freezing is one of the known symptoms of the problem covered by that repair extension). If indicated, you can contact the nearest
Apple Authorized Service Provider (AASP) to arrange for a replacement logic board.
If your eMac doesn't appear to be one of those possiblly affected by the bad capacitor problem, please post back with some additional information: how much space is there on the hard drive? How much RAM does the Mac have? What OS version? When you tried to reinstall from the OS X Install disc, was this the install disc that came with the eMac? If so, had you ever upgraded the base version of the OS since getting the Mac (e.g., upgrading from 10.3.x to 10.4.x)?
You may be able to keep the Mac running a bit longer than one minute in order to check it's settings and drive space and the like by
Starting Up in Safe Mode.