The Time-Turners were destroyed at the end of the fifth book, hence they were still intact at the fourth. Well, why not use one immediately to go back in time and prevent Harry and Cedric from touching the Triwizard Cup? I think that going back a few hours in time wouldn't have been so disastrous as happened 20 years later, by Albus and Scorpius.
Was Cedric's life cheaper than Sirius and Buckbeak's lives?
There are two answers to this.
1)
There are strict regulations about the use of the time turner. They had to jump through hoops to get a time turner for Hermione to study, and then at the end of PoA Harry and Hermione use it in a way they were not supposed to.
The time turner was, as far as I know, returned to the ministry.
If they wanted to use a time turner at the end of this, they would have to get the ministry's permission, and at the point they'd be asking for a time turner, the ministry has already drawn a line of competition. Fudge is starting to think Dumbledore is after him and his job with his lies about Voldemort. Fudge doesn't want voldemort to be back, so won't want to see proof. Even without the suspicion of Dumbledore's motivation, why would the ministry let them save cedric? How many other people have died and they not used a time turner?
2)
Because they didn't use a time turner to save Cedric.
By that I mean, the events that occur in PoA when we follow hermione and harry back in time to save sirius are actually no different to the events that occurred when we followed Harry, Ron and Hermione the first time around - we just see them from a different perspective. First time around we hear what we think is buckbeak being executed, second time around we see buckbeak was never there. First time around we see what we thought might have been harry's dad casting a patronus, second time around we realise it was harry saving himself.
If they were going to go back in time to save cedric, cedric would have been saved first time around.
Time travel in harry potter doesn't change the past, it just leads to the travellers fulfilling their part in events that have already happened.
"You'll find it's a very small universe when I'm angry with you"
1) Not convincing. If they had that power at their disposal, they would jump through hoops if it meant saving a life. To expand on that, if a 12 year old girl can so casually get her hands on such a device and use it with no supervision, it defies reason that the relevant magical effect could not be used again, in any shape or form, by anyone at this point in time onward. This is simply a giant plot hole in the entire series.
2) This only explains how we know a time-turner wasn't (successfully) used to save Cedric, not why, so it doesn't actually answer the question. We might have seen different events had someone in the future decided to use one.
Besides, according to the butterfly effect, you couldn't turn back time without changing it.
1) Your comment reads like you are determined to see a giant plot hole. So it probably won't make much difference for me to respond, or maybe it's just the way I read what you've written.
In case I am wrong... that's not the way in the wizarding world. They accept that death is a part of life, and even in tragedy, the wizarding world accepts that going back to save lives leads you down a dangerous path. Acceptance of death is one of the overarching themes of the series - from the first book where Harry was at risk of wasting away in front of the mirror of erised if he didn't accept his parents were gone, through to the final book where Harry is only able to defeat Voldemort by accepting death. Conversely, the bad guy is the one trying to avoid death, to rule and control death.
Because they accept death, they don't move heaven and earth to save anyone who dies.
The ministry keep a strict control over the time turners.
The school had to apply for one and really go to bat for Hermione, who used it under strict instruction not to let anyone know - including her two best friends. At the end of PoA, she gave it back because she quit divination and no longer needed it, so the time turner was returned to the ministry. Dumbledore and Harry didn't have a time turner to use illegitimately (as they did in PoA).
Given how the ministry reacted to Harry letting them know Voldemort was back (including the campaign against Dumbledore that plays out in OotP), coupled with a wider position of the wizarding world that death cannot and should not be undone, and that going back in time to change things is generally bad*, it would have been nigh on impossible to convince them to use a time turner to go back. Why would they? What makes Cedric so much more important than all the other people who died?
Dumbledore et al would need to move against the ministry to get a time turner, pootentially sacrificing Dumbledore and/or Harry - the only people capable of defeating Voldemort - all for what? Some random kid.
Cedric doesn't offer anything to the ministry or to Dumbledore (a man who, lest we forget, is at this point in the story raising Harry to sacrifice him in a long term plan to defeat Voldemort)
2) It's a time travel paradox. If they haven't gone back they can't go back. There is no 'first time' where someone eventually decides to use one. There is only destiny (ironically, given another theme in the book is choices).
*
Yes, the butterfly effect - something that (alongside the previously mentioned acceptance of death) would factor into the ministry not allowing people to go back and save some random child. If they go back and save Cedric, the butterfly effect could lead to another child dying, so they'd have to go back to save that child, which would lead to someone else dying, and so on. Or perhaps it leads to muggles wiping out the wizarding world, or Dragons eating all the wizarding gold, or everyone having lizard tongues.
"You'll find it's a very small universe when I'm angry with you"