You can useCarbon Copy Cloner to copy everything from the working eMac onto the non-working eMac while the working eMac is running. If your eMac will still do target mode into the working one, you can download the above software, select the booted drive as the source drive, and your eMac's drive as the target, however it is possible this will not work.
When you say your eMac crashed, what exactly happened? It is possible that the hard drive in your eMac failed or is failing, so in order to get it running again you would need to replace the hard drive. On the eMac, this repair is somewhat involved, and you have to be very careful because it exposes the CRT, which has several areas which can be extremely dangerous to touch if not properly handled. CRTs retain a great deal of voltage, even when unplugged, sometimes for weeks, and they can give you a nasty shock if you touch them in the wrong place.
Also keep in mind that cloning from the working computer to the non-working computer will ERASE any data that you have stored on that eMac, so if you don't have it backed up anywhere, you may want to attempt that with target mode before proceeding.
Good luck!