Scenario: a valid search warrant is executed on John Doe and his computer is seized. Somehow, this manages to net the police Doe's passwords for a bunch of sites (for example, Doe stored all his usernames and password in an unencrypted spreadsheet file rather than using a proper password manager). Do the police need to get a new warrant to use those passwords to gain access to all of Doe's accounts?
Yes, assuming that the original warrant doesn't include such accounts. Suppose the warrant includes the premise and everything in it. That includes his computer, and the files, with or without passwords. It does not include his office, his safe deposit box, or his off-site files on Drape-box, with or without passwords. In other words, it's about the scope of the warrant. It may be that in the course of the search they uncovered probable cause that they did not previously had, that would allow inclusion of off-site files – hence they can get a new warrant. Or, the police may have suddenly realized "Shucks, we should have asked for a warrant that allows us to search Drape-box".