Moved this to Malware Discussion > Home User Assistance for better attention.
It's quite possible you would transfer the infection so I would clean it off the old machine first.
First way would be to try System Restore to before it all happened....if successful, temporarily disable System Restore and the infected files will be gone.
If not successful try this removal guide, it's a good one and the source is very reputable: http://www.bleepingcomputer.com/virus-removal/remove-fbi-monkeypak-ransomware
Quoting from that removal guide is some important advice:
This infection is typically installed onto a computer when the user visits a hacked web site that contains malicious scripts that exploit vulnerabilities on the computer to install the FBI Ransomware without their knowledge or permission. It is for these reasons that it is imperative that all computer users make sure their installed programs, including Windows, are up-to-date with the latest patches. Later in this guide we will outline a method that can be used to make sure your programs are all updated and safe.