This FBI warning thing is particularly annoying. This is a known malware scam often called "ransomware" because payment is demanded. First thing, as said elsewhere, DO NOT PAY!
Removal can be easy or tricky as there are several variants of this code.
You can read more about this at:
http://botcrawl.com/how-to-remove-the-fbi-moneypak-ransomware-virus-fake-fbi-malware-removal/ Basically if you have access to your computer, you can run System Restore to bring your system back to a point before the malware was installed. This removes enough of the malware to keep it from activating, but it does not totally remove all files installed. To do this, you should a malware removal tool. While many are available, most security professionals like MalwareBytes which is available for download and use free of charge. Run the full scan option and remove anything MalwareBytes finds.
If you cannot access your computer, even in Safe Mode with Command Prompt on Windows, you may have to recover from a recovery disk. The article above mentions a number of ways to do this.
The key points are that this is just malware, it is a scam, it can infect your computer and can be very scary.
Also, just because it has gone dormant does not mean it is gone or you need not worry more about it. Many variants continue monitoring your system. It is even possible that some of the email hacking you have heard about or even may have experienced could be traced back to this malware, which is technically a Trojan. I would strongly suggest you try to remove this malware, even if it appears to have mysteriously "vanished" or you no longer experience evidence of it on your system.
Best of luck to all