iMac 2011 as a second screen MacBook Pro 2022.

That will not work for two reasons:

1) The 2011 iMac must be in 100% working order.

2) The 2022 M2 MacBook Pro does not support Target Display Mode.

Carefully read > Use your iMac as a display with target display mode - Apple Support

The wise thing to do (as you have likely discovered) is to simply buy an external display for the 2022 MBP. External displays are much better because:

• Simple to setup
• Dead reliable
• No expensive software or licensing needed
• Cheap, they start at less than $100
• No expensive cabling needed

You can't. Software solutions would require a working Mac, and Target Display Mode is dead for new Macs.

+1 to what Keith Barkley posted . target Display mode is dead for all recent Macs..,plus you need a working Mac to even try , and your iMac isn’t working… try doing Recovery mode on your iMac first, reboot holding down Apple+R keys together on its keyboard ; use a usb wired keyboard and mouse on your iMac… you should see a language screen, pick one and continue… to get to Mac OS Tools, move your arrow to the top centre of your screen… run Disk Utility, if your hard drive /ssd is OK, reinstall macOS… if it needs minor fixing, let Dudk Utility do it, then try reinstalling Mac OS.. if Disk Utility can’t fix it, then you’re gonna have to buy an app/software to do that; probably… if it CAN fix it, that is, if not, your HD/ssd is probably hosed - needs replacing… the only way to do what you suggest/hope is a 3rd party device called Duet Display( $150) … a 27” hdmi monitor ( even used+’in good condition) could be had for $100-ish

john B

OldGoat67 wrote:

the only way to do what you suggest/hope is a 3rd party device called Duet Display( $150)

You might be thinking of Luna Display (Astropad). That one involves a device. Duet Display is a "subscription" (rental) program that costs $4/month ("Duet Air") to $6/month ("Duet Pro").