What type of malware can, for example, locks up a user's computer and then display a message that purports to come from a law enforcement agency that states the user must pay a fine for illegal activity?

Ransomware

Explanation:

Ransomware is a type of malicious software that blocks access to a computer system or data, usually by encrypting it, until the victim pays a fee to the attacker. In many cases, the ransom demand comes with a deadline. If the victim doesn't pay in time, the data is gone forever.