I connected an HDMI cable to my 40" HDTV that I use as a monitor, normally in VGA mode. I then took photos of the same block of text in a Website. The first image is the photo taken from the monitor when I was using the VGA cable. The text is red and the background was a light salmon. You can see the red of the letters bleed into the background. On this monitor, I can even see a small amount of ringing. As an example, the flashing line cursor at the insertion point of this post looks like a second, faint cursor just to the right of the primary cursor. I am using a high quality cable and video card. It's definitely the monitor causing the ringing.
This second photo is the same on-screen image but in HDMI mode. I took the HDMI photo first. I created a screenshot while in HDMI mode and then pasted the screenshot into a document that was visible on the VGA input of the same monitor. I had to crop the image to make it small enough to post and the camera was closer to the screen when I took the VGA version.
You should be able to see the halos around the letters in the second image. If not, change he distance between you and the monitor. On a 40" monitor, I have to back away a little or blur my vision a little to get the individual pixels to come together.
What I believe I'm seeing is a limitation of the monitor trying to show high contrast changes that occur at adjacent pixels. This is what I'm referring to as ringing except that my initial description is based on a video system that scans the screen (VGA and older), like the old CRTs did. It appears to me that the monitor just doesn't have the video bandwidth to display the image properly. The monitor might be trying to smooth the image but I believe it's just poor bandwidth. I don't have any Blue Ray discs to make comparisons with and NTSC DVDs have a lower bandwidth than VGA so they won't work. Even so, I'll bet a Blue Ray would look OK on this monitor due to lower bandwidth (more gradual contrast changes) of the Blue Ray video and/or the player.
I don't believe the problem is with the video card, as this is the third different card that I've used on this monitor and they all do the same thing.
It could still possibly be the cable. I don't have more than one cable or monitor to test with.
I think it would be worth while for you to take the computer and cable to a store that sells TVs to make comparisons. Maybe even connect to a 4K HDTV. I'll bet you can find a reasonably priced TV/monitor that will work with VGA and maybe even with HDMI (not 4K).