Error Code 4400:011A

Like an idiot, I did no backup of anything.  

I am in the process of moving and was hoping to run across the disk to reinstall the operating system.  I found this and wondered if it is what I need.

That appears to be a Win 7 disk, but the questions are:

1. Did your system come with Vista or Win 7 preinstalled by Dell?
2. Is it a full Win 7 installation disk or just a disk to upgrade from Vista to Win 7?
3. Even if it's a full Win 7 disk, if your system came with Vista, the product key on the sticker may only activate reinstallation of Vista. So you'd have to install Vista first and upgrade to Win 7.

If you don't have a backup of your files, are you prepared to lose everything? You might consider purchasing a new hard drive and installing Windows on it. Then install the old one as a secondary drive so you can rescue your files. You could eventually reformat the old drive and use it for additional storage.

That appears to be a full Win 7 installation disk, so you should be able to reinstall by booting from that disk.

You could try a running a Win 7 repair after booting from that disk, rather than a full reinstall, but I don't know if a repair will work after recovering from a failed Win 10 upgrade. The disk doesn't say it includes Service Pack 1, so if you had SP1 installed on the hard drive, it may not be possible to do a repair with this disk, meaning only a clean install from disk and then installing SP1 which you can download from Microsoft (free) followed by all the other Microsoft Win 7 updates and fixes.

You'll have to decide if you're willing to lose all your files or if they're not backed up on external media. Otherwise, you can either install this hard drive in another PC (or in a drive enclosure) so you can rescue your files first. Or install a new hard drive in this PC and do a clean Win 7 install and then reinstall the old drive as secondary so you can retrieve your data.