cable(s) to migrate between imacs?

If your old iMac will start in Target Disk Mode you'll need a Thunderbolt 3 to Thunderbolt 2 adapter Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple

a Thunderbolt 2 to Firewire adapter Apple Thunderbolt to FireWire Adapter - Apple

and finally your Firewire 800cable.

Follow the steps here How to use target disk mode to move files to another computer - Apple Support

If your computer won't start at all because of a hardware failure other than the hard disk, or if the disk has failed you're in for more work.

The old computer will not boot so you cannot connect directly to it to migrate. If you backed up the old computer using Time Machine, then it's simple. Connect the old computer's Time Machine via a USB cable to the new computer, Setup Assistant will launch the first time you turn on a new Mac, it will get to a point where it asks if you are migrating from another Mac, select yes and migrate from the Time Machine backup. If you happen to create a bootable clone of the old computer using either SuperDuper! or Carbon Copy Cloner the same process will work.

If you never backed up the old computer (Please do so going forward!!!!!!!!!!!!!!!!!!!!!!!!!!!) remove the old computer's HD and install it in an enclosure and use Migration Assistant to migrate from that.

Those are the options that will work, otherwise you cannot get any data off the old computer!