Well,
It is not over yet, but it will cost another card to even buy the lab PSU you are going to need...
The good news is that I found
a picture of the back of a similar card and there is nothing there on that empty 10-pin pad nearby. But it is low quality and hard to see what else is there.
The step-downs marked as AMCF are
NB671LBGQ (
Datasheet) and are not very expensive I think you will need to get at least one.
The
IR3555s are not very expensive either, you will need 8 in the worst case. You might need the controller too - Digi+ ASP1300 (rebranded
IR3567B).
The pad can be repaired, but if there is an inter-layer short circuit - this card is a junk.
So far I see no issues with memory phases so those might be OK but do not start. It might be due to something wrong with the up1641P (can't find it anywhere but
here) memory power controller or just the power-up sequence does not get there. The memory ICs showing expected resistance.
The problem would be to find out the value of the shot capacitor on the back (will have to take off and measure one like that from another memory chip... now, you need a tool to measure ceramic capacitors). The ripped off part is probably another capacitor, but again, the only way to find out for sure is to check one of the other memory IC wirings or get a working card of the same type. Worst case, in addition to the parts in the back, you will have to get a memory IC upfront (
HYNIX GDDR5 H5GQ2H24MFR-T2C ) and it takes a matrix to seat this guy properly.
The sad part is - only after getting all the power phases working, we will find out if the core chip is OK.
Will only know better when you take most of them off for which you need tools and skills.
If you are doing all this just to get a working card, you better off buying one. I can send you a working 1060 for say the same 150$.
If it is for joy - let's keep going when you get the tools, there are lots to do 🙃