installing OS onto my 2008 24 imac

Hi all. I have an early 2008 (8,1) 24 inch IMac. It developed issues a year ago when updating the OS I think. At the time I went ahead and picked up a new machine for the family. I took a crack earlier this week at getting the 24 inch going again. I found the original 10.5 install disks. My first attempt I managed to get 10.5 running and updated to the extent it would update. However...I cant find the 10.6 physical disk to get it to Snow Leopard...thus enabling easy download and upgrading to say...10.11 On my second attempt..I tried a full restore (picking a date forward enough in Time Machine from my external G Drive) to get to 10.8 No luck ..even though it said it installed..it wouldn't boot. No matter on the personal files on the 24...they are on other Macs. I was just looking to get the OS to a point that I could use the OS upgrade from Apple. So..now my machine pretty much has nothing on the drive...or at least it will when I use the disk Util again. My question is this....is there a way to get my 24 inch back running without having to buy the physical Snow Leopard disk? I have a new Mac sitting beside the old and would like a clean install of an OS that the Early 2008 will handle.