Why didn't Jack ask for help when Elizabeth cuffed him?

It's never confirmed, but there are several possibilities here.

1. The captain goes down with the ship.

Pirates are shown to be adamant about sticking to the code. The one pirate who said "screw the code" was killed immediately (by Captain Teague).

2. Jack begrudgingly agrees.

Note that Elizabeth tells Jack why she does it: the Kraken is coming for him, not anyone else. It's possible Jack agrees here. He still tries to escape, but still separates himself from the group.

3. There wouldn't be enough time to save him, it would get more people killed.

Jack may also have considered that the Kraken was going to appear any second, and that rescuing him (hearing Jack, going back, trying to free him, possibly having to fight Elizabeth in the process, ...) is going to take so much time that it was going to get them all killed.

Jack was going to the locker, but I'm not sure if the others were guaranteed an afterlife. While he doesn't particularly show it, Jack does care about his friends to some degree.

4. The plot demanded it.

It never happened because the plot required Jack to be taken down to the locker. Either the writers forgot about the possibility (unlikely), or the writers simply omitted the pointless attempt to free Jack because it wasn't supposed to succeed anyway (much more likely) and it kept screentime to a minimum.

5. It was the end of the second movie, with a clear message that a third movie would be released.

This seems the most plausible explanation, in my opinion.

Consider that the crew being unaware to Elizabeth having betrayed Jack serves as a cliffhanger for the third movie (here's a double cliffhanger because Will ends up seeing Elizabeth kiss Jack and thinks he's being cheated on).

If Jack had screamed about Elizabeth chaining him to the mast, both cliffhangers would not have existed.

It's thematic and apart of the story structure:

A speculative answer based on the story is that the first three POTC films set up a redemption arc for Captain Jack Sparrow, whom over the course of his life has left people in precarious situations leading up to his involvement with Will Turner, Bootstrap Bill, and Elizabeth Swann.

A redemption arc is a story where the character goes through many obstacles and makes up for something bad they have done. For example, a bad guy might be evil at the beginning of a story but by the end of the story he saves the world and becomes good.

It's in the newer films (On Stranger Tides, Dead Men Tell No Tales) have begun to delve further and further into Jack's past after facing his fears in Davy Jones' Locker (At World's End), while in the fifth film begins to revisit the horrible situation that occurs at the end of At World's End, where Will is separated from Elizabeth and must uphold the duties of the Flying Dutchmen, which was the only way to save Will Turner's life. Pirates of the Caribbean features a series of tragic, unrequited, and unresolved love stories.

Pirates of the Caribbean: Dead Man's Chest - Script

                                 ELIZABETH SWANN
                     Because you and I *are* alike, and there 
                     will come a moment when you have a chance 
                     to show it. To do the right thing.


                                 JACK SPARROW
                     I *love* those moments. I like to wave 
                     at them as they pass by.

                                 ELIZABETH SWANN
                     You'll have the chance to do something... 
                     something courageous. And when you do, 
                     you'll discover something: that you're 
                     a good man.

                                 JACK SPARROW
                     All evidence to the contrary.

                                 ELIZABETH SWANN
                     I have faith in you. Want to know why?


                                 JACK SPARROW
                     Do tell, dearie.

                                 ELIZABETH SWANN
                     Curiosity. You're going to want it. 
                     A chance to be admired. And gain the 
                     rewards that follow. You won't be able 
                     to resist. You're going to want to know... 
                     what it tastes like.

                                 JACK SPARROW
                     I *do* want to know what it tastes like.


                                 ELIZABETH SWANN
                     But - seeing as you're a good man I 
                     know you will *never* put me in a position 
                     that would compromise my honor.

In the second film the story dances around if Jack can corrupt Elizabeth's fidelity and nobility, while she challenges Jack to be a better man and take the high road. So Elizabeth betrays Will in one instance, and Jack doesn't fight the argument Elizabeth proposes when she says, "This is the only way.", and Jack stays on the ship, slips out of his cuffs, and dies fighting the Kraken.