Hi doodlebug
Well..... "so much depends".... (there was a Wallace Steven's verse that opened with those lines, prescient poet that he was...)
So much depends.... on the age of the PC, and especially - the number of handy-dandy manufacturer utilities (power saving, fan control, device driver updates, remote support apps) .... The in-place upgrades (as opposed to "clean installs") are the likeliest to experience difficulties, because they are the most likely to have software written badly by manufacturers who don't update the darn things often enough... and that not-so-great software ends up causing no end of trouble in a new operating system such as Windows 10.
One simple way to test this:
1) Create a backup system image to an external drive (they are down to $50 for 1 TB lately)
2) Create a bootable Windows 10 DVD with the Media Creation Tool.
3) Use the DVD to clean install Windows 10. If you've linked your current Windows 10 installation to your Microsoft account, you won't have to enter your product key - Microsoft will already have it "on file". If not, use the product key either from your latest Windows 10 install, or simply use your previous Windows 7/8.1 key again.
To rule out "Murphy's Law", though, I'd recommend using the builtin Dell Diagnostics to make sure that it isn't a coincidental hardware failure underneath the software errors. There are instructions in your Dell manuals, and on the Dell support site for your model. Here's a generic example of the multiple ways to run the diagnostics (quite a few are available just by visiting their site) ---
What Dell diagnostic tools can I use to fix hardware problems? | Dell US
If you happen to have a model with both Intel onboard video and a discrete Nvidia card, check out this thread:
Solved BSOD Kernel Security Check Failure consistently caused by Photoshop... - Windows 10 Forums
... That thread mentions Photoshop as needing the more powerful graphics, but I'd imagine any advanced & demanding program might have similar graphics settings.
Another quick fix (especially if the above link doesn't apply to your situation, or simply doesn't work)... is to try limiting optional programs that run at startup, especially handy-dandys from Dell... (you can simply temporarily disable them from the Startup tab in Task Manager)... And some users find that a Bios update can help an older motherboard get along better with Windows 10 ...
Let us know how things go ... and if you need help deciding which troubleshooting steps to try next.