First, you eMac's processor has to be 1.0Ghz or faster to install Leopard.
Second, the disk cannot be a gray system install/restore disk from another Mac model. A proper Leopard retail install disk looks like this:
Third, you need a min of 512MB RAM. Some eMacs shipped with a lot less.
Try booting while holding the c key depressed until you see a desktop. That forces the computer to boot from a system disc in the optical drive and should bring up the installer.
You can install a max. RAM of 2 GBs.
OS X 10.5 Leopard will run appreciably better on 2 GBs of RAM.
Hhere are the specs for the RAM.
2.0 GB (Actual) 1.0 GB (Apple) Memory Slots 2 - PC-2700 DDR333 184-pin SDRAM
You can find and purchase reliable Mac RAM from online Mac RAM vendors Crucial memory or OWC (macsales).
Crucial does not recognize that eMac model's ability to accomodate 1GB Modules:
They tend to stick wth Apple specs regardless of how outdated the specs.
Go with OWC. We bought their 1GB module for our eMac 1.42Ghz about two years ago and it has worked perfectly, This is their listing for the one I bought: