First, looks like you have a Graphite iMac. Second, since the iMac starts up and looks for an OS, the basic hardware is working. Now, it just needs that OS! Tiger is a possibility. See this page for compatibility:
http://www.apple.com/macosx/upgrade/requirements.html You should have no problem running Tiger on this iMac if it has enough RAM, but you may need to order a CD (not DVD) if the mac is in deed of the CD-RW variety. You will need to purchase the Tiger DVD and send to Apple a printed copy of the "Tiger Media Exchange" form
http://images.apple.com/macosx/pdf/tigermediaexchangev3.pdf along with the DVD. They will send you a CD version. If you live near an Apple store, you should ask the folks there what your options are and they may be able to tell you if the mac has a DVD drive. Regardless, if you purchase Tiger, try the DVD and if it is recognized by the iMac, you are good to go! If not recognized, then exchange for CD.