If the Snow Leopard disc was an upgrade over Leopard, a drop-in
limited installer that shipped with some computers, it may not be
able to fully boot the computer for complete installation. If it is a
retail version, & not an upgrade drop-in, it'd be evidently marked.
Learn about troubleshooting Mac OS X installation from CD or DVD. ...
Learn about troubleshooting Mac OS X ... work with Mac OS X, you may need to install ...
support.apple.com/en-us/HT201817
If your computer shipped with Snow Leopard 10.6.x on grey-label
DVD media, to get a replacement from Apple (from AppleCare, etc
main online or by support phone) is a practical step. While an Apple
retail Store with Genius may be able to install Snow Leopard 10.6
it may not be the as-shipped kit with original software extras.
U.S. iPod, Mac and iPad technical support:
(800) APL–CARE (800–275–2273)
Contact - How to Contact Us - Apple:
https://www.apple.com/contact/
You may be able to arrange an appointment with an official Apple store
genius for them to help check the computer. However if you get a new
replacement hard disk drive, and install it into the computer (or use a
cable adapter kit, to format a replacement before taking the Macintosh
apart; then once a new OS X is installed and tested in replacement HDD
the new drive could be swapped for the old one.) Once a new drive is
installed in the computer, the old one could be accessed by use of the
same 'universal USB drive adapter' such as OWC macsales shows on
site. A non-bootable drive that may have damages, can still be seen by
a computer to try & extract files off later.
•NewerTech Universal Drive Adapter USB: (incl. cables + power adapter)
https://eshop.macsales.com/item/NewerTech/U3NVSPATA/
examples of replacement internal hard drives & solid-state options:
https://eshop.macsales.com/shop/internal_storage/hard_drives_and_SSD
When replacing an old hard disk drive, you may consider to also replace
the cables; and be careful because the connectors can break. And more
details may be involved. See iFixit.com site for suitable Mac repair guide.
• iMac Intel Repair Guides - iFixit:
https://www.ifixit.com/Device/iMac_Intel
Note some build models of iMac require a similar Apple part number HDD
that has similar sensor inside, or a correct cable to use the right drive, so
the cooling fans don't run high speed; without the sensor being seen by
iMac hardware, fans will run. OWC offered an update kit with sensor to use
with those iMacs. You can also contact a reputable reseller to simply ask
questions, and note OWC macsales.com has several parts, & online guides;
you can find these by Mac model, https://eshop.macsales.com/upgrades/
Sorry to say that at this late (near 2AM local time) I'm unable to suggest a
simple method of talking your iMac into working. You may try the Opt key
(or X) instead of C key, so it can try to start from any startup disc or drive.
• What to Do when OS X install DVDs won't work:
https://duckduckgo.com/?q=what+to+do+when+OS+X+install+DVDs+won%27t+work&ia=web
• Shortcuts you can use while your Mac is starting up - Apple Support
• Mac keyboard shortcuts - Apple Support
A generalized list of handy startup options + shortcuts for Macs that run OS X:
https://www.engadget.com/2014/04/21/mac-101-a-handy-list-of-startup-options-for- macs-running-os-x/
https://www.engadget.com/2006/03/27/tuaw-tip-keyboard-shortcuts-during-mac-os-x- startup/
In any event...
Good luck & happy trails! 🙂