Is the system still under warranty?
If both cards show up in the Device Manager (i.e. you have two HD5900 entries) do either have a yellow notification triangle attached? If no then...
Check your drivers. The latest whql drivers are
Catalyst 11.3 (this is the Vista/Win7 64-bit version) -if you do not have them I would suggest you install. Also install the ATI Catalyst Application Profiles application 11.3CAP1 (this the CrossfireX addition). There is an 11.4 preview driver, but at this point in time I would suggest you stick with WHQL signed drivers.
Download
GPU-Z. Run the program and click on the "Sensors" tab to make sure everything is being recorded. Click the second card from the dropdown tab (lower left hand corner) and check the readings of this also. If you are unsure of what you are seeing then post a screenshot. Probably best to have two instances of GPU-Z running -one for each card.
if all seems fine there then...
Have your power supply checked -I would do this in any case, since the power draw of your system is substantial ( 150-200w CPU/chipset + 2 x 300w HD5970's - assuming nothing is OC'ed). I would get the supply checked professionally, and since the system is prebuilt I would assume that the cabling is routed and possibly secured in place- so unless you feel confident in unplugging the cables (24 pin motherboard, 8 pin EPS12V, video card cables, SATA power, molex for watercooling etc.) AND reinstalling them later I'd get the whole system in front of someone qualified with a voltmeter/multimeter (maybe a house call to avoid needing to re-bleed the watercooling loop). Depending on the chassis and where the radiator placement is you might have difficulty removing the PSU in any event.
Post back once you have checked off the list and can provide some more info.