I want to give away my eMac and reset to factory settings but... CD player doesn't read discs and it won't register an external drive. What should I do?

One way could possibly be to use FireWire Target Disk Mode (for example, described on page 27 in https://manuals.info.apple.com/MANUALS/0/MA476/en_US/eMac_OriginalUserGuide.pdf). The eMac could be chosen as the target computer or a host, depending upon how you wish to carry out the work.

Or...

Open System Preferences>Accounts, unlock the lock, click on the little plus icon, make a new admin account, log out & into the new account.

In the same pref pane highlight your old account, click the little minus icon, then use Disk Utility to Secure Erase Free Space.