Is my IC broken if Q1 == !Q1
If you refer to the truth table on Page 10 of the datasheet (section 7.4), the answer to your question is simply, no, it's almost certainly not broken.



Notice that when Set and Reset are both high, then both Q and Q` are also high, therefore both outputs being high is not on its own an indicator of being "broken".

When left floating, the value of a 4000 series logic IC input is in a completely unknown state. It may represent a high value, or it may represent a low value. The protection circuitry on the input will pull it to somewhere mid-supply due to reverse leakage currents in the clamping diodes.

In your case it is likely representing a high level as without any other evidence this would account for the behaviour you are seeing.