I don't necessarily mean the video - kernel panics are rarely to do with something that far removed from the CPU. I mean test the hardware of your computer.
I'll do the testing suggested. The machine is rather old. HP Compaq dc5800 sff (small form factor) I would not be surprised if the kernel just did not like my motherboard any more.
It is very rare that old motherboards (or rather chipsets) stop being supported - I have CentOS 7 running on 10, 15 yr old kit. You get a lot more problems with new motherboards than you get with old ones.
Even after I figure out the kermal panics, the video will still be an issue.
They may well be linked.
First, check the memory - MemTest86+ is the tool most people use for this. Run it on your system and it will highlight memory problems. It can be found at www.memtest.org - the precompiled versions are tiny and will fit on a floppy (or memory stick or CD).
If that doesn't detect anything try running a hardware diagnostic - there's a load on the UBCD (www.ultimatebootcd.com) or Hiren's BootCD ( www.hiren.info). You might want to download one of those anyway as they both contain MemTest86+.
None of this needs you to open the case.
That is good.
My suspicion is that this is a repeat of what sent me to Centos from Fedora. (Yes I know the relationship). I'm told I couldn't install Fedora on a machine because a kernel bug affected precisely one kind of motherboard, mine. I'm also told the bug was supposedly fixed, but I was never able to run any later Fedora on that machine.
You never mentioned that you had previously had issues with Fedora on the machine - not even when I suggested you run a Live version of Fedora to provide different drivers. Not even when you got kernel panics when booting the live Fedora did you mention this was a known issue.
P.