Chosen Solution
I got this iMac (EMC 2133) that has been standing for 4 years in a box. Virtually new. I didn’t remember any particular problems, but I decided to format it and update it to use it a little… surprise .. I format, I start the installation and it starts to reboot in a convulsive manner. I thought the pendrive was bad, and I used the original Mac OS X Leopard disks… it seemed to work, and then it restarted for no reason. Now I decided to open it and in the end I said to myself, let’s have a clean, CPU / GPU paste change doesn’t hurt, and a quick check on the battery (it was at 2.90v) and capacitors … I’m sure I haven’t solved anything, and I’ve started writing here. The capacitors all seem ok, but I’m not 100% sure … I ask for advice and help … Update (08/08/2021) In the end, I substituted the thermally conductive paste on: CPU / GPU / Chipset / Power supply diode bridge (which was detached from its cooling fin). I kept the battery unplugged for a few hours, and to be honest I put the same back. I keep it in test for a couple of days and see what it does, otherwise I change it.
You are likely hitting a few different issues! First having the system tucked away for so long likely has a dead PRAM battery as the battery is not designed to support the system that long without being plugged in iMac Intel 20" EMC 2133 and 2210 PRAM Battery Replacement What is the OS version you are trying to install? The highest version your system will support is El Capitan (OS-X 10.11.x) As far as rebooting during the OS install process your system may do that as your systems firmware is often also updated depending what it was running. You also have a newer file system (HFS to HFS+) which could also be a factor. You also could be facing an issue with your power supply! Capacitor Plague So you may need either a new power supply with the better caps or will need to replace the electrolytic capacitors if they show signs of failing.