Then you will need to go to iFixit and check out the relevant guide for this iMac. They will have instructions on how to disassemble the iMac and retrieve the hard drive.
Depending on what iMac model you have. and if it only has a power supply issue it may be worth repairing. So you need to make this decision on how much care you take when you disassemble the iMac e.g. Remembering where each part goes.
Once the hard drive has been retrieved. You will need some kind of enclosure so you can connect it to your new computer / other computer. You could get a cheap USB3 Enclosure or Adapter or Hard Drive Dock.
I like the NewerTech® Universal Drive Adapter and NewerTech® Voyager Productline. Have one of each there both great.
Those or similar devices or a external enclosure will allow you to connect the drive to another computer. Once connected and given the hard drive is all okay you can just transfer your data manually or use another method. E.g. Something like Apple's migration assistant if it's going on a new Mac.
Thanks again for the help!
iMac is about 8 years old, and I just don't want to spend much on it, seeing as I just plunked down $2K on a new macbook and external drive. Although, I'd consider reviving it if the power supply were cheaply replaced and I could wipe the old iMac and give it to my kids or such.
My old imac is dead, but I want to access the data on the hard drive to back it up to an external drive. How can I do this? I don't intend to revive it, just get the data from the drive.