I looked at the pins while slowly inserting sd card. All of them moved as the card was being inserted. However, one of them was bent a little different that the others. I changed it's shape while sd card was partially inserted. When doing that, I accidentally took off one of the cables from battery. I have resoldered it.
I turned it on and sd card started working. It is fixed.
Now I don't know if bending the pin helped or if cutting the power did it, but I am guessing it was the pin, as I think I have tried hardware shutdown (hold power for 10-15 seconds) before and didn't fix anything.