2011 27-inch iMac screen failure: Is it worth repairing & how do I backup data & prep for selling?

Hello, 

I have a 2011iMac (purchased in 2012) that is not currently working, and want to determine if it is worth me repairing at this point. My instinct is that based on the age alone and my intended use, it is not, however I'd appreciate any input. 

Background info: my iMac was included in the Graphics card recall program around 2013-14 and Apple replaced my failed graphics card accordingly.

I hadn't really experienced any other issues with the system since then, until around May of last year.

When I tried to start up the computer, the screen remained black & I got the two-three continuous beeps signifying an error. 

I'd investigated the issue, determined what the beeps I was receiving signified & acted accordingly.

Specifically, I did a PRAM reset amongst a few other reset options. 

Ultimately, I was able to resolve(at least temporarily) the issue related to the beeps, as my computer began starting up as normal. However, throughout all of these tests and the following few weeks, the screen always remained black and never appeared visible. 

As I'd seen suggested, I attempted to look at my screen, at the right angle with a flashlight, to verify if I could see anything being displayed below the screen, but was unable to see anything myself.

Recently, I decided to have a local computer store/repair place check it out & provide a diagnostic on it - they were unable to specifically determine what the exact issue was, but laid out an action plan on the order of parts/components they would begin to replace/repair to pinpoint the issue in the most cost effective method.

Their first plan (amongst other general recommendations, such as upgrading the drive from an HDD to an SSD, etc.) was to attempt to replace the screen, using a third-party, aftermarket company.

Note, the tech specialist hooked up my iMac to an external display using thunderbolt to HDMI & was able to see my desktop, log-in and use my system.

He just advised me on some things re: the age of my system, and that it's OS and hardware is outdated, and would be recommended to upgrade/replace, if possible.

At this point, as I've been working from home for over 1-year, the non-functioning iMac is simply taking up room on my limited workspace. I want to determine if it would be most logical/cost-effective for me to simply sell it for parts/repair or, if I should attempt to repair it and use it primarily as a general system for internet exploring and, most primarily, an external monitor/screen in conjunction with my (16-inch, Version 11.2.3) 2019 MacBook pro. Based on the estimate for the screen repair alone ($180 - 300$ I believe), this does not seem logical/worth it, especially considering it will not be under any long-time warranty, etc.

And lastly, I'd like to verify how, if I move forward with selling the iMac for parts/repair, that I would go about backing up my hard drive and also formatting/wiping the drive so that it is safe for selling.

I'm familiar with removing the drives themselves from MacBooks and other computers, and simply connecting them to an ESata drive reader to backup, and have no hesitation doing so, however, would I not need to do additional steps to ensure the drive and system are completely safe and wiped for selling as well?

Additionally, I've read about target disk mode, but am not completely clear on if this mode would allow me to view my 2011 iMac through my 2019 USB-C based MacBook, and still backup/wipe the drive & iMac and successfully prepare for selling.

I know I've provided a laundry list of questions, notes and concerns, but any advice you all are able to provide is greatly appreciated.

Thanks and iMac computer details are listed below:

27-inch iMac

Part Number: Z0M7

With the following configuration:

•3.4GHz Quad-Core Intel Core i7

•16GB 1333MHz DDR3 SDRAM - 4x4GB

•2TB Serial ATA Drive

•AMD Radeon HD 6970M 2GB GDDR5