Can I retrieve data from an iMac Pro that won't turn on

If your Mac doesn't turn on - Apple Support

Methodically exhaust each one of those steps. If you eventually conclude the iMac is dead with no possibility of repair and needs to be replaced, the usual way to recover the broken one's data is to restore a Time Machine backup.

The inability to easily recover data from a SSD is not a shortcoming of Apple, it's due to the way the ssd technology stores data. In many instances, recovering data from a HDD can also be extremely difficult if not impossible for consumers, too. If this were any other PC brand the same would hold true.

The only way to safeguard against data loss is to have a rigorous back up strategy.

Apple makes it very easy to back up our stuff by including their Time Machine back up software preinstalled on all Mac computers, but they can't hand hold each of us and make us use best practices. All that is required is an external drive and a few minutes of our time to set it into motion.

Back up your Mac with Time Machine - Apple Support

You were on the right track when you previously backed up your Mac. It's unfortunate that you didn't continue. Hopefully you won't lose too much stuff.

The iMac Pro uses SSD storage that is unconventional. There is no way to access that if the machine won't boot.

I assume that you did not take advantage of the Time Machine backup app included with the macOS, so there is no practical way to recover your data.

Please see: how to Upgrade iMac Pro SSD (Replace Storage): EveryMac.com

The same inability to retrieve data exists for iPhones and iPads; they are built the same way. They just don't have the equivalent of Time Machine, which has been included with every Mac OS version for about two decades now.

SndanceKid wrote:

Turns out I did back it up a few months ago. Anyway, now my question is, if I buy a new iMac with the M4 chip, can I use my backup info from the iMac Pro to rebuild my desktop, programs, etc?

Yes. If that backup drive and the data it holds are in working order, then there is no reason to believe you cannot recover all of your files that are on it.

If you used Time Machine to create that backup, then you can use Migration Assistant on your new Mac to restore those files. When you’re ready to setup your new Mac the easiest and most reliable way to migrate your data and files from the old Mac is simply to connect the old Mac's Time Machine backup drive to the new Mac before you turn it on for the first time. (You may need a USB-A to USB-C adapter for this; easily found online for ~$10 or less.) 

When you start your new Mac for the first time it will launch Setup Assistant and lead you through the setup process. Eventually Setup Assistant will ask if you are migrating from another computer or Time Machine backup. You are, so select that option and follow the on-screen prompts to completion.

If you used another method of backing up the old iMac, then once you have setup the new Mac, you can either install a copy of the application you used previously - perhaps Carbon Copy Cloner or SuperDuper! - and use that to recover your files, or you may even be able to simply drag-n-drop your files from the backup drive onto your new Mac.

I guess my question is, in situations like this, is it usually the power supply?

Yes, very often it is the power supply that fails, especially if the cause was a fail of the mains.