as rma is out of question and u are open to zip tie an 80mm fan if this doesnt work,
1.u might as well try to make a hole at the center of the fan with a heated screwdriver or something along those lines.
chances are the bearing is not exposed to prevent dust accumulation.
2.if u can see the bearing after making the hole.use viscous lubricant.make sure its viscous enough so that it doesnt drip into the heatsink and eventually on the gpu core.
3.looking at your photos,i would clean the heat sink too.chances are it aint running cause of dust.
4.did u check the fan connections?the female plug from ur fan and the male port on the pcb?it usually doesnt happen,but when its good if u check it.
PS - i had bought a xfx 5770 in march this year and it stopped working last month.i thought of opening it but then saw the stickers so i sent it for rma.
after a 2 week delay and a lot of yelling(i live in india,and here they are heavily understaffed so unless u dont yell,u wont get your card on time!),i got a 6770.the same thing but with hdmi 1.4 and AMD instead of ATi.so if they agree for a ram,u might get a 6770.