Upgrade graphic card or buy new iMac

That would be a challenge, I think. When my PS went, I opened up the iMac, & removed the HDD. Got a hard drive docking station (as well as having a Carbon Copy clone) to copy any stuff over from an older OS X partition if needed. Maybe an option would be to review these Apple links from 'Using Time Machine to back up or restore your Mac':

Restore everything:

• To restore everything in your Time Machine backup, use macOS Recovery.
• To copy the files, settings, and user accounts in your backup to another Mac, use Migration Assistant.

Transferring date from the broken iMac to a new one is easy if the old iMac will start in Target Disk Mode Move your content to a new Mac - Apple Support and Use target disk mode to share files between two Mac computers - Apple Support

I've not been able to find one; here is some info on the USB C port/adapter:

https://www.apple.com/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt- 2-adapter

https://support.apple.com/en-us/HT207266

I'd probably check with someone at a Genius Bar or call Apple support to ask about that (or try the online store chat referencing the usb c adapter.

A replacement GPU won't be cheap as they are all custom made

(beware of places like EBAY as you could be getting one in any

manner of condition).

You could take a chance and do it, as you said it is not working anyway,

but you would need to add the cost of that card (and tools) to a replacement

Mac.

Personally, I would replace the Mac with a newer one and donate the

broken one to some electronics technician school (vo-tech maybe) or

properly recycle.

I was facing the same type of situation; power supply went out, which meant a new logic board. Return on investment was a key factor --- went with a 27" iMac, so I can upgrade RAM as needed, and CarbonCopy'd the old iMac over to the new one. I had upgraded to macOS Sierra on the old one previously, worked great. So happy I went that route! The 17,1 iMac is great.

FireWire 800 to Thunderbolt 2, you mean...

No FireWire to Thunderbolt 3 (wich is the new standard).

Is there a recomended way to connect FireWire to Thunderbolt 3 ? There is no Thunderbolt 2 anymore in new macs!

funny thing mine is a 2011 also and the screen has lines in it and wont start up. Keeps trying to restart...does yours ? It cost me a lot and I don't think I'll ever own one again. I also maxed out the ram. Too bad. I think I am going to trash it

what did you end up doing may I ask. The same thing has happened to me, I have a 2011 mid, 27 inch 3.4 ghz quad core Sandy Bridge with 20 gb of ram. I am just curious as to what you did. I don't want to start over and I have windows based laptop but I love my imac. Please write back...thanks. Here in MN it is about $500 to replace but then other parts could go and this not a good graphics card anyway?

There is a thunderbolt > firewire adapter.

Apple Thunderbolt to FireWire Adapter - Apple

you may want to look into this

BIZON – United States | External graphics card (eGPU) for Apple MacBook, Mac Pro, mac mini, iMac. EGPU. eGFX USB-C GPU D…

Yes, we know.

But, as Target Disk Mode works just with FireWire (am I wrong?)... How do you plug the target disk to new macs, with no Firewire? (Not a word in Apple Support)