Having a model number or a link to a description of the video card would be more useful than a picture of the video card. I can't determine any info about the card other than what I can see in the picture. That in mind, if you say the card works in your old HP workstation, I'll believe it.
Do you know for certain that everything in the new computer works (minus that video card)? Since that motherboard has onboard video, there's a chance that its BIOS are set to use the onboard and to NOT use an external graphics card. If everything else IS working correctly and you attach your monitor to the motherboard's display outputs you *should* get a working system - just with no R7 250X video card. If this does not result in a working computer, you have an issue with some other component(s).
One of my theories is that, even though the HP power supply is rated at 600W, it may not be providing enough of the correct voltages to power your new system. Power supply design has changed a lot since the Pentium 4 days (a google search indicated that the xw8200 uses a Pentium 4 based Xeon).
Another worst-case possibility is that even if the power supply plugs all fit in the newer motherboard, the pinouts may be different. I've seen this on some HP, Dell, etc systems that are around this age. If this is the case there is a chance that connecting the old power supply to the new motherboard has fried everything.
At this point there are still too many unknowns for me to suggest any one course of action. Any additional details you can provide as to the exact parts you are using as well as exactly what configurations you've tried will be helpful in diagnosing what's going on.
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