Near the end of Harry Potter and the Goblet of Fire in the chapter "Veritaserum", Barty Crouch Jr. drinks Veritaserum and the rise of Voldemort is now undoubtedly clear and easy to understand. There are no more missing peaces. Dumbledore, Snape, Harry, Professor McGonagall, Sirius (in dog form) and Winky all hear Crouch's testament under Veritaserum.
When Fudge arrives with a Dementor for protection, the Dementor kisses Crouch, making him unable to drink Veritaserum again. Fudge does not believe Harry and wants Crouch's proof before he believes that Voldemort has returned. Obviously Harry cannot take Veritaserum as the Ministry thinks he is hallucinating plus he has secrets (Invisibility Cloak, Marauder's Map) so he does not want to get Fred and George into trouble.
Dumbledore is also too valuable to take Veritaserum. Snape is a spy and obviously he can't. Sirius is on the run so obviously he cannot show himself. Winky is owned by no one at the end of GoF, but she still works for Hogwarts. Dumbledore could order Winky to drink Veritaserum. Ministry leaders may be biased against Winky because she is a house-elf, but that is proof. If not, McGonagall has no secrets (that's what I think) and she can drink Veritaserum. Of course she will need convincing but I think she will if it is for the convincing of the Ministry. If not Winky is there.