Welcome to the forums..That's a tough one to call given the age of the components, could be the mobo
or the graphics card (unlikely the PSU would be at fault)..The only way to know for sure would be to try the 9800 GTX+ in another system or try another compatibil graphics card in your 780i..If you know somebody that would be willing to try your 9800 GTX+ in their system, that would be ideal..Or, you could take it to a PC repair shop and have them test it.
Realize that solder cracking on the PCB of graphics cards manufactured in that era was relatively common and lead to a Pandora's box of issues, but mostly artifacting and BSOD's, betting that's the problem though..You could try disassembling the card and baking only the PCB
like this which should reflow any solder cracks that might exist..If you decide to bake it, do it with the GPU side up,
not down as shown in the video..I just link that video because the band/song (Come Clarity - In Flames) seems appropriate, lol..Remove the fiber optic power indicator conduit that goes from the PCB to the mounting bracket or it will melt, trust me on that one, lol..Otherwise, baking won't hurt anything at all..If it's still under warranty, RMA it if you determin that it's failed, of course.