I don't think I would ever pay ransom under any circumstances. Not for data or system functionality. I'd throw the computers in the river. I know this about myself because I had to deal with a kidnapping and extortion of my best friend in south america around 15 years ago.. and a few years later a ddos extortion attempt on one of my servers (the criminal was released from prison recently and I won a federal judgment…
How do we go from here? Your job as a negotiator is to get them get them off their "fight mode" through the use of time, dialogue, and empathy.
By saying "I wont negotiate" you're building a gloom vision that there is no future. If the threat is real, you're out of time and out of luck. As Voss says, "She's dead"*
Further readings:
Stalling for Time: My Life as an FBI Hostage Negotiator ( by Gary Noesner)
Never Split the Difference (Chris Voss)
Ego, Authority, Failure (Derek Gaunt)
Movie: A Hijacking (IMDB)
* "60 seconds or she dies" challenge on Youtube (Chris Voss).