2006 iMac 2Ghz 512mb Core Duo will not boot.

Did your system come with the Grey CD/DVD disks? Or, did it come with a Retail version of Mac OS-X Leopard 10.5.8"? Which is the highest OS this system will run. You’ll need to find the disks to re-install the OS as it does sound like the OS installed is corrupted.

As to using this system as long as its not used on the internet then you’ll be safe. If you are thinking of using it on the internet you’ll encounter both issue with the Web browser as this is such an old system no one is making a modern version which supports HTML 5. Even if you are just using it for email it would be risky as there are a lot of security breaches in this OS level. Lastly you won’t be able to run any Intel based applications only PowerPC versions which have long since left the market place.

So the bottom line: This is not a very good system for your grandson - Sorry ;-{

I would recommend getting a ChromeBook laptop or tablet as a better investment Should I Buy a Chromebook? Buying Guide and Advice. Or look at getting a newer used Apple system. If you can find a MacBook or MacBook Pro 2007 or newer that would be better or a iMac 2009 or newer.

Looking through the links I’ve posted here you can find the system you have found used to check out the OS support (look at the bottom of the given entry) You really don’t want a system that it only supports Mavericks MacOS 10.9 as the highest supported OS.