Kay, did you go get a mine from the supply place? It's in the same screen as the mansion, I think (memory, memory)
You can use that mine in a room with the robots- I used it in Broadstreets chamber (I think) and it discombumulated those robots. That gave me 3 power cells to use for other things. Eventually, I got another one from the supply and used it on the robots in the village too.
You can only pick up one power cell at a time.
Can you identify everything in your inventory. I was running around stuck when it turned out I have a ground mine in my inventory and just did not realize it