Thank you for reply.
I thought you suggestion was reasonable so I touched everything I could on this board with soldering iron. Interestingly, it still does not reliably work but it's "less broken" now. Previously it needed continuous pressure on PCB to even turn on. Now, after pressing on PCB I was able to play with this for a minute or two before it hanged. Maybe it was still warm, though. Anyway, I was trying to apply pressure in different areas and it seems to react best on direct pushing on Sirf IC (BGA). I'll probably have my hot-air station on Wednesday so I am still waiting for suggestions what should I do not to screw this up. (wont be a huge loss, since device does not work anyway, but if I can rescue it then cool). For now I am attaching some photos of the PCB for curious readers.