Just took the ram out 1 stick at a time no go.
When you get down to the last stick, take it out and put one of the others back in.
Long shot, but worth ruling out as much as possible.
After that, the screen is 100% tested as working, and ram is unlikely to be the issue...
Is the graphics card built into the motherboard or discrete?
If it's discrete and you have another suitable card, from another computer, that you can swap with for testing, try that,
or if it's discrete but your motherboard happens to have built in VGA/DVI output, try the built in.
Also, if the GPU is discrete and it has power cables, make sure they're seated properly and haven't come loose.
If the GPU is onboard, are there two ports? Some computers back then had VGA + DVI, sometimes on an auxiliary PCI-E card?
Basically if you have the option to swap anything, try that.
With lights and fans and evidence of power, I would doubt the PSU or motherboard being faulty.
Never say never, but I'd be looking at everything else first.
My troubleshooting would go like this, in order.
Connections inside computer - Screen - Cables - Ram - GPU (if possible) - CPU.
How much of this you're able to test and check depends on what you have available to you, and how tech-handy you are.
I mean, you could literally pick up a newer faster machine at the amenity site; I get that,
but I also get that it's a pain setting up a working environment from scratch. I like to fix things if I can.
As I say, even with a dead drive the computer should boot and throw you an error but, if it's convenient, I guess you could pull the power connector at the hard drive and try to boot.
Super long shot but, as always, worth ruling anything and everything out.
Edit: I guess you would have mentioned it but did anything happen before it died?
Did it take a bang or a knock, or was there a power cut, or...anything out of the ordinary?