5770 artifacting all over the place ..

Looks like you got a bad card. What you should do is exchange it for a new one.

If this is too much effort or simply out of the question, then what you want to do is get a program like MSI Afterburner. If possible, increase the voltage by 0.02V and see if that helps. If it doesn't help or isn't possible, lower you GPU core clock by 10-50mhz. If that doesn't help, you can try lowering the core clock as well. But, at this point, you should realize that the card isn't running as advertised, so really the best option is to get a new card that will work properly.

Also, what PSU do you have? It might be a power issue (tho I doubt it)

EDIT: Could also be that you need higher clocks for 2D. In that case, the solution would be the exact opposite. Open CCC and go to ATI Overdrive tab, then overclock the cards. Only do it enough to get the idle clocks up. Not sure what the 5770 idles at, but my 5850s idle at 157/300 and if I use CCC to OC a bit, the idle clocks then go to 400/900. You might want to try this solution first, actually.