LED lights coming on, no matter what component it is, graphics card, motherboard, etc., generally never means much of anything EXCEPT if there are none on. Then it means the problem, whatever it is, is worse than if the lights were on, but even with them on it means very little because the circuits that power those LED lights are usually separate from the rest of the functional system. The exception would be for any CPU, Memory or GPU error LEDs.
I don't see any mention of what motherboard you have, but given the fact that the graphics card is about 7 years old, since that is when the GTX 770's were released (Not even remotely possible that it's only 1.5 years old. Minimum it could realistically be is six year and most probably it is seven years old) then that is the MOST probable suspect/culprit. Obviously this is something that could be a motherboard or power supply issue but I'm betting it's the graphics card.
Pull the graphics card out and see if you get anything at all, fans, other lights, beeps (If you have a system speaker installed) or try a different graphics card if anybody you know has one that you can borrow for the purpose of testing. Obviously, this is the simplest of tests you will encounter since all it entails is swapping out the card for another one. I'd bet favorably that it's the graphics card but I wouldn't bet the house on it.