^ OK, sorry I misunderstood, because earlier you said "As of right, both the Radeon 5450 and the GeForce are both connected to the motherboard." So you moved both the card AND the power supply to this computer then. What wattage is the PSU you're using?
You didn't find any BIOS setting to control the default graphics card, I take it. And you're sure you have the latest BIOS flashed for that computer? Actually, I just checked the specs, which say "Integrated video is not available if a graphics card is installed." To me that suggests installing a video card will override the default one automatically. So, maybe it's not sensing the new one properly.
I did notice in one of the photos of the
Radeon HD 5450 512MB that there's an internal DVI socket. Connecting up a monitor should be external, and I see there is an external one. Maybe it's for the option where the motherboard is installed inside a single casing that has the LCD display.
One other thing... check the feedback for this video card on New Egg (link above). I spotted one of them that said this:
Cons: Has issues with older motherboards. I couldn't get it to recognize the video card at all on my MSI 945GM3 motherboard. Some googling found some people have good luck, others get motherboard BIOS upgrades, and the rest of us are out of luck.
Just because this card worked with your other power supply in the other computer, doesn't mean it'll work fine in this current computer. The system may have different power requirements and tax the power supply enough so that there's not enough left for the card.
Cons: Review of this card claimed it was a low wattage video card. Upon arrival, system requirements mentioned on carton advised minimum power requirement was 400 watts. Being that my desktop only has a 250 watt power supply, this card wouldn't worrk for me.