What problems did William and Mary have ruling together?
== == None really. Although Mary was declared co-soveriegn by virtue of the fact that she was the one with an actual claim to the throne, in actual fact William was the one who ruled and made all royal decisions.
When did England have no ruling king?
from 1653 - 1658 England was ruled by Oliver Cromwell, who overthrew the monarchy and cut off the former King, Charles the 1st's, head. England also had no ruling king during the reigns of her ruling queens Mary I and Mary II ( tho Mary II co-ruled with William) Elizabeth I Victoria and Elizabeth II , the current Monarch.