The restore disk will work on the old eMac, I remember working on those things, they looked as big and bulky as they really are.
The eMacs had two major issues with them.
- Sound card failed. It was a known issue, and Apple at the time if you had your cert, allowed you to repair them.
- The CD drive failed. Which it sounds like your may of, if you can read other CDs then it may be that the CDs that it came with either is not compatible with the machine or the firmware may of been updated, and caused the computer to no longer recognize the disks as compatible. Which sometimes was a known issue.
On a side note you never stated how you were attempting to get your computer into booting from the CD... there are multiple ways to try.
The easiest way to see if the disk are even being recognized as a boot disk is as the computer is starting to press and hold down the shift key while the computer is booting. Don't let go until the screen shows all drives that are bootable.
If your CDs are ever going to be recognizable it is going to be here.
Also, and I hate to say this, but make sure you have the correct CD in when you start up, otherwise I really can't guarantee you will ever see the CD.
You can also eject the CD from this screen as well, so if it doesn't show up, you should be able to eject the CD from there, and try other disk.
If this doesn't work, really your only other choice is getting a friend with an old computer and external HD case and install the OS on the drive.
To get to the drive you need to unscrew the back, if I remember correctly they were still using star bits back then, #5 I believe. I may be wrong, but if you need help taking the computer apart ask, I may be able to still get the repair guide for the eMac and tell you how to fix any issues hardware wise you may have with it.
Best Answer
For every OS X 'delta' release - 10.10.1/2/3/ ...10.10.4 etc - which App Store will download to each Mac there is a simultaneous 'combo' update release which rolls up all the previous deltas into one single downloadable update.
It was for many years considered the 'pro' way to do the update, as it can also correct potential update issues that the delta can't.
You can always find updates related to OS X here.
As the combo update doesn't use the App Store "download, install, delete" structure, you can pass it from machine to machine at your leisure.
Maybe not as slick as using the server - but it's free ;-)
From comments -
The combo update can also be applied to machines which are already running the current version of the OS, unlike the App Store's delta "update" mechanism. This can sometimes correct issues that may linger after doing a series of incremental [delta] updates.
The combo updater is invariably larger than the incremental updates; but it is worth it, just for the peace of mind.