iMac 8.1 time machine won't complete backup

i have a 2008 iMac 8.1, 2.4 ghz, 4 gigs ram. I upgraded to Yosemite and the machine was so slow it essentially wouldn't work at all. I tried to revert to a pre upgrade version using time machine , it erased the main drive, them the restore quit before installing the startup file. Now I am screwed and it won't start without an install disk. I get a message that the machine can't install the OS. this happens over and over again. Using the disk utility, the diagnostic says the disk ISPs ok, but doesn't have a startup file, I can't ejecttheinstall. Disk or install a time machine backup. I am caught in a loop that will not allo this machine to work.

When the reinstall quits, it shows a error log, but I do not know what to look for or what it means.

help!!!!!