Dell XPS 430s and Radeon HD 6770+6670 problem

I have two Dell XPS 430s, and here are their specs:

XPS 320 1:

original Dell XPS 430 Motherboard(x48chipset w/DDR3 dual channel support), case(with fans, heatsink, front panel, etc.) and Teac front panel Card Reader with BlueTooth

Intel Core 2 Quad QX9650(3Ghz, 12MB L2 cache, (P)LGA775)

4 x 2 sticks DDR3-1333 RAM (8GB total)

XFX PRO 550 Watt Full Wired 80+ Bronze PSU core edition power supply

Intel 320 series 80GB SATA II SSD

Seagate Barracuda SATA II 160GB 7200RPM Hard Drive

TP-link PCI wireless N-300MBPS Wireless Network Adapter

Quite Old PCI 5-port USB 2.0 card

PCIe NIC x1 2-port USB 2.0 card

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Dell XPS 430 2:

original Dell XPS 430 Motherboard(x48chipset w/DDR3 dual channel support), case(with fans, heatsink, front panel, etc.) and Dell 375 Watt Power Supply

Intel Core 2 Quad QX9650(3Ghz, 12MB L2 cache, (P)LGA775)

4 x 2 sticks DDR3-1333 RAM (8GB total)

500 GB 7200 RPM HDD

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Everything works GREAT in EVERY WAY. And I mean EVERY way I can POSSIBLE IMAGINE it is supposed to work in.

except:

I have a XFX HD-667X-ZAF3 AMD Radeon HD 6670(800Mhz cpre clock, 1 Ghz clock on the 1GB GDDR5)

and

An ASUS AMD Radeon HD 6770(850Mhz Core Clock, 1.2 Ghz clock on the 1 GB GDDR5).

When I try to use either of them with either XPS 430, the computer's fans spin and the lights come on, but nothing else happens. I have tried everything. By everything, I mean everything that I can think of. And, no matter how what things are connected, the same thing happens when I put one of those cards in one of the XPS 430 motherboards. It is to be noted that the CPU fan comes on at the highest speed, which is very loud. The HD 6770 has one 6pin power connector; when it is connected to a PSU as it should be through that, what I described happens, as usual. If I have the card plugged into the board, but leave the 6pin connector disconnected, it behaves as it normally should with no graphics card in it(which is normal; a card does not activate if it requires a connector for power but does not have it connected). I have tried the computers with different cards that I have, and they work fine with either my Dell OEM Radeon X600 or my Dell OEM Radeon HD 5450. Using those cards, I have been able to confirm that everything else concerning those XPS 430s works just perfectly, and I am happy with the x48 chipset with DDR3. I just don't understand why those HD 6XXX series cards don't work.

Please help if you have any ideas!