Late 2009 imac as external monitor with a new M4 Mac Mini

27" Late 2009 Macs support Target Display Mode using Mini DisplayPort input.

Their Technical Specifications say that they support DisplayPort input, and there are no sneaky footnotes in those specifications saying that the input must be only from other old Macs. The implication was that those iMacs could act as displays for any DisplayPort-compliant video source that could present a signal with appropriate resolution. However, Apple later added restrictions such that the video source has to be a Mac with a hardware model year of 2019 or earlier, running Catalina or earlier. The M4 Mac mini is too new on both counts.

See the bad news here: Use your iMac as a display with target display mode – Apple Support

Thus, according to Apple's Support document, you can't use either of your 27" iMacs as Target Displays for a M4 Mac mini. Officially, you need a real display of some sort, such as a monitor, HDTV / UHDTV, or projector.

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That said, I have seen one or two threads where people reported success in using a 27" 2009 iMac, or a 27" 2010 iMac (I forget which), as a Target Display. Those were the years before iMacs got Thunderbolt (and thus, the years when TDM only required DisplayPort input instead of the harder-to-obtain Thunderbolt input).

So you might be able to use a 27" Late 2009 iMac that has a good graphics card as a Target Display, with the aid of a USB-C to Mini DisplayPort adapter cable (or equivalent). If it works, it will be unsupported, and you will need to be prepared for the chance that a macOS update could break your setup at any time, forcing you to buy a real monitor. But who knows, you might get lucky, and it might be "Christmas."

I do not think there is any chance of this working with the 27" Late 2009 iMac that has a bad graphics card. All of the video data that comes into an iMac in Target Display Mode will be going through that iMac's GPU on the way to the screen. The M4 Mac mini's GPU may have done all the work of compositing multiple objects into a series of single, large, bitmaps; but if the iMac's faulty GPU cannot render those bitmaps on the iMac's screen, all of the M4 mini's GPU's work will have gone for naught.

No. Not for a Mac M4. Too new.

Yes, for older Mac configurations.

https://support.apple.com/en-us/105126

+1 No.

New Mac's including the Mac mini's do not support using an old iMac as a display.

If you have or get a new Mac mini, then you need to use an external display.

see > Connect a display to Mac mini.

You "could" use Screen Sharing to utilize the operable iMac as a display for the mini ... however ...

You will still need a regular display to set up the mini & test screen sharing.

You will also need an HDMI dummy plug for the mini once it is set up ... and

The shared screen image on the iMac will not be as satisfactory as a display plugged directly into the mini

IMHO the right thing to do is get a decent display for the mini ... and recycle the old iMacs.

Note that when the 27" Late 2009 iMac came out, a Dell 27" display with the same resolution (2560x1440 pixels) sold for something like $1200 (list price) / $1000 (on sale).

According to an inflation calculator, $1000 in 2009 USD is roughly equivalent to $1516 in 2026 USD. That inflation-adjusted amount of money would be almost enough to buy you a 27" Apple 5K Studio Display – one with twice the linear resolution of the screens on the 27" Late 2009 iMacs.

There are also a number of good 27" 4K (3840x2160 pixel) monitors that go for $300 – $400 USD, or so. Although these aren't quite as sharp as the 27" 5K Apple Studio Display, a 27" 4K display running in "like 2560x1440" mode will render things in finer detail than an actual 27" 2560x1440 screen like the ones in your old iMacs.

So replacing the working 27" Late 2009 iMac with a real hardware monitor now does not need to be anywhere near as expensive as it would have been when that iMac was new.

Nope!