When you find yourself trying to remember a show (or any works) that's on the tip of your tongue but just out of reach, come here - the collective brain of the TVTropes community can probably help. Post all the details you can remember (examples help). If you're looking for a trope, head over to Trope Finder. Have general questions about tropes? Visit Ask The Tropers!
Being strapped to a chair with eyelids held open is a famous scene from A Clockwork Orange, so if it wasn't that film then it was likely an homage to that scene. Maybe that will help you find it.
There's one Eerie, Indiana episode that involves a teacher brainwashing students with an open-eye machine.
"And as long as a sack of shit is not a good thing to be, chivalry will never die."^^ There is a page for references to that scene - The Ludovico Technique
So, I remember when I was little kid (probably around '02-'03 but I could easily be wrong) there was this movie that kind of caught my eye on TV, but the only thing I can remember is this one scene where a guy was looking at what appeared to be confidential information on an old computer monitor, but it looked like he was confused and had the wrong program or something (again, I was really young so sadly I don't know if my memory's serving me right here). I believe it started off with some sort of simplistic DOS-looking animation until it was cut by a logo of sorts (I remember it being the FBI's), then he's suddenly looking at a list of sorts. Cue a gentleman or two in suits coming into his apartment and shooting him.
The second was much more recent, at least three years ago at most. I only started watching near the end, but there was a kid strapped to a chair and his eyelids were held open. It was clear he was being brainwashed, and I think a teacher in his school was behind it. The whole thing was confusing out of context. He eventually broke out, and a bunch of high school kids (one of which was definitely a jock) led by said teacher was sent to chase him down. Don't remember how everything went after that, sadly. This one had a stereotypical 80s-cheese movie vibe to it.
I'm sorry I don't remember much detail about either of these movies, but any kind of lead would be great!