As am I .

Under normal circumstances I'd say the problem was that the onboard graphics haven't been disabled, but the fact that the HD 5770 works in the slot would seem to rule that out.
I can't find a Gateway BIOS manual so I assume the board is using a stock Intel BIOS.
A quick browse of the Intel specific options shows...

Screenshot is a quick mashup in Paint - original source here
From the description for the "PCIE x16 Link Retrain" it seems as though non-detection can be card specific. Past this info I can't be too sure how to advise on troubleshooting since I'm not familiar with your BIOS layout/options.
I would suggest possibly flashing the BIOS (if you think it's worth the risk) and definitely updating the chipset drivers once you have a card installed and OS up and running.

Oh, and "Blackest Eyes".

The point is that this card was being detected before. All of a sudden there seems to be an issue. This is what the OP said:

If you haven't reset your bios, go ahead and try.

To quote Arthur Conan Doyle: "...you have eliminated the impossible, whatever remains, however improbable, must be the truth?" (Sign of the Four, 1890)
So looking at it logically...
We have effectively ruled out a dead card/bad socket pins
We have effectively ruled out a malfunctioning PCI-E slot
We have effectively ruled out lack of power delivery as being the cause
The motherboard works

What we do have is an error/warning message in the BIOS

All this would lead me to believe that the boards BIOS is not using the same settings as it did when the card was previously installed. The BIOS probably isn't corrupted since that should show a checksum error or hang (and is functioning ok with the HD 5770 installed).
The BIOS error message seems reasonably specific and is applicable to the one area of the BIOS that the OP hasn't been able to access (onboard graphics).
Why one video card would automatically disable the onboard video, while another card will not seems implausible, but in the absence of any other avenue that I can see, what other course of action can be taken?

@hk
Check post #10.
The OP says that in his troubleshooting he had cleared CMOS and "reset BIOS defaults" -which I presume is the same as "load optimised defaults"

Hi all, just been reading this and I am having the exact same problem. One minute it was working fine, restarted the PC and it wasn't. Tried everything! The card seems to be working fine its just not outputting anything and I can't stop the PC booting to the onboard graphics (even though PCI Express is selected in the BIOS). Is there a way to disable the onboard graphics other than uninstalling the drivers? I'm worried that if there is, and the card doesn't work, I'll be stuck without any and never be able to see it again!

@ adsheff - I suggest you start a fresh thread detailing exactly what happened. Have you tested your card on another working system to determine that it's functioning OK?