You should be able to connect old PC's HDMI-OUT port to HDMI-IN on the Inspiron 5410 AIO. You will need to use the button on the AIO to select the HDMI-IN port as the source of the video signal. If you don't have another monitor connected directly to old PC, you'll always have to turn AIO on just to use that old PC.  Probably good idea to power AIO on first, before powering on old PC. And then use the button to change the input source. Compatibility Mode is strictly a Microsoft Windows thing, so Dell won't talk about it. Windows has a built-in Compatibility Troubleshooter which can help you run software designed for a previous OS, assuming you have the installation disk(s) and product key(s). You can't just copy software files over from one PC onto another one. Apps have to be installed into Windows on that other PC. Have you looked on line to see if you can download the installer for any of your old software, without needing installation disks, assuming you have their product keys?  FWIW, I'm running MS Office 2003 (originally for XP), on my Win 10 desktop without using a Compatibility Mode. You might need to use a Compatibility Mode with MS Office '97. I'm also running an app designed for Win 95 in Win 10 by having compatibility set for Win 7, without problems. You could consider LibreOffice (free) in Win 11 or OpenOffice (free). (NOTE: LibreOffice seems to get updated regularly, but OpenOffice may not be getting updated.)  Both have "Office" applications that mimic MS Word, Excel, PowerPoint, etc, and read/write MS Office file formats, so they're compatible with your existing MS Office files and can create/save new files in Office format.  I have LibreOffice on my laptop and move files back/forth to Office 2003 on my desktop with no problems.  
Using Inspiron 5410 as a monitor for another desktop