Your iMac year and model can only go as high as OS X 10.7.5 Lion.
You will need to increase the amount of RAM in your iMac model to 4 GBs of whIch your iMac model will only recognize 3.2-3.4 GB of the total RAM.
OS X runs better with matched pairs of RAM installed.
Correct, compatible and reliable Mac RAM can ONLY be purchased from online RAM sources Crucial memory or OWC (http://www.macsales.com).
Before embarking on a major OS upgrade, it would be wise, advisable and very prudent if you have a good,working backup of your current system to an external connected and Mac formatted Flash drive OR externally connected USB, Thunderbolt or FireWire 800, Mac formatted hard drive. Then, use either OS X Time Machine app to backup your entire system to the external drive OR purchase, install and use a data cloning app, like CarbonCopyCloner or SuperDuper, to make an exact and bootable copy (clone) of your entire Mac's internal hard drive. This step is really needed in case something goes wrong with the install of the new OS or you simply do not like the new OS, you have a very easy way/procedure to return your Mac to its former working state.
Then, determine if your Mac meets ALL minimum system install requirements.
Mac OS X v10.6 Snow Leopard system requirements
Purchased Installer disc here.
http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard
To install Snow Leopard for the first time, you must have a Mac with:
An Intel processor
An internal or external DVD drive, or DVD or CD Sharing
At least 1 GB of RAM (additional RAM is recommended)
A built-in display or a display connected to an Apple-supplied video card supported by your computer
At least 5 GB of disk space available, or 7 GB of disk space if you install the developer tools.
Then use the OS X Software Update feature of OS X 19.6.3, located in the System Preferences Panel to update your iMac to OS X 10.6.8 and to updated all other installed Apple software and security updates.
OS X 10.7 Lion system requirements
Purchased emailed download code here.
http://store.apple.com/us/product/D6106Z/A/os-x-lion
To use OS X 10.7 Lion, make sure your computer has the following:
An Intel Core 2 Duo, Core i3, Core i5, Core i7, or Xeon processor
Mac OS X v10.6.6 or later to install via the Mac App Store (v10.6.8 recommended)
7 GB of available disk space
2 GB of RAM