I'm running Lubuntu 16.04 on an old Dell Optiplex 780 with an E7500 and integragrated graphics (GMA 4500). When scrolling and during video playback I get this weird wave form tear in the middle of the screen. I first used the VGA out, then tried the DVI out from a PCI adapter and the issue persists.
Your Dell isn't all that old. The integrated graphics ought to work fine on Ubuntu.
I work on old gear all the time. The first thing I do when I get a new-to-me box is upgrade the BIOS. Since your current setup isn't working all that well for you, I'd do that as a first step.
I didn't go on to the Dell web site to look at your particular model but there may be graphics related updates and release notes there that indicate problems with that particular mobo.
Assuming your issue isn't a design problem that Dell has an upgrade for, I'd slip in a known good PCI graphics card to see if that fixes your problem. Used graphics cards can be had from recyclers for around $5.
Not sure what you mean by a DVI out from a PCI adapter. Perhaps you already did the above-mentioned step.
Of course video cables and the monitor itself should be looked at and eliminated as a potential problem.
Seems pretty unlikely that the problem you have is Ubuntu related but I suppose anything is possible. 16.04 LTS has served me very well for quite a long time. On many computers using many different graphics setups. Zero problems so far.