2008 imac stuck in reboot loop

My 2008 iMac is stuck in a reboot loop. Having a backup, I attempted to reinstall OS X but it wouldn't recognize the thumb drive or DVD. So, using Target Disk Mode, I reinstalled OSX from a mac mini. I can boot into single user mode, and obviously target disk mode. I can boot the mac mini from the disk in the iMac so it isn't the hard drive. The progress meter gets a little over half way and then it reboots. Verbose mode also gets stuck in startup loop.

Is it safe to assume that the logic board is not failing given that single user mode seems to work fine?

Is this indicative of a failing graphics card?

It looks as good as the day I bought it and it is hard to set it aside. I replaced the HD with an SSD about 3 years ago which made it much more usable. I had installed the patch from DOSdude1.com to run high sierra. It ran fine for a couple weeks. One day the display got all wonky: colors were inverted and image became striated but the mouse pointer was still moving. Then it wouldn't boot. I didn't 100% trust the patch even though it may be harmless so went the route to move backwards through the steps to reinstall El Capitan.