What version iMac? What Mac OSX version?
Please do "About this Mac" under your Apple menu and post what it shows for OSX version and the processor type. The processor wil sort your computer into one of teh four braod families of iMac made since 1998.
FWIW, this forum is for iMacs made before 2006. We need to get you moved if your processor type contains the name "intel."
What is it?
Your setup is:
ethernet modem > ethernet cable > iMac -----> ipad
Seems like this would work. The iMac is acting like a wireless router. It doesn't know what is connecting to it.
I'd buy a wifi router. Will save on you iMac wear & tear. HD's don't last forever.
I would not pay over $70 for one. I found mine for $5 when compusa was goin out of business.