Why did Lord Cutler Beckett not give the order to fire/attack?

He was shocked by fact that he lost the Dutchman. And has not chance of winning the battle and even to come alive which was sure victory situation at start.

From wikia:

Despite losing the Flying Dutchman, Beckett remains confident of his victory and takes out the Endeavour to destroy the Black Pearl personally. Jack, to everyone's surprise, orders the crew to hold all canvas (sails) and not run. As the Endeavour approaches the Pearl, the Flying Dutchman suddenly resurfaces and Beckett is happy as he believes that the ship is still on his side. Unknown to him, the ship is under the command of its new captain, Will Turner and is now on the pirates' side. The ship and crew revert to their original forms and Will orders his new crew to ready the ship's weapons. Jack orders the same thing and the Black Pearl and the Flying Dutchman begin a double broadside on the Endeavour. Beckett was so shocked, he is unable to give orders. This forced his second-in command, Lieutenant Groves, to give the order to abandon ship. Some of the crew do so, but Beckett remains on board. The double broadside penetrates the power magazine, destroying the Endeavour in a series of massive explosions and killing Cutler Beckett.

This scene is probably what bothered me most about the entire movie. A ship like the Endeavour has over a hundred guns, the cream of which is 15x 32 pounders and 14x 24 pounders per side. Not to mention a significantly thicker hull due to it being a ship of the line (built to take punishment in the line of battle).

The Black Pearl, being a brig East Indiaman / Galleon, would have a broadside of about 16x 9 pounders (32 guns total) (Jack even confirmed this, giving the order to "lay out the nines"). The Flying Dutchman looks to be similarly armed, though a century older in design. Neither ship would even be able to dent the Endeavour with a single broadside, whereas a point-blank broadside from the Endeavour would have sent the Black Pearl back to the bottom of the sea. I get that the Dutchman is a magic ship that can't be sunk, but it has not ever shown itself to be immune to being torn to shreds - Will would have had to be captain of a few chunks of wood.

Given the inability to miss at point-blank range, being flanked by the two smaller and less well armed vessels was the best position Cutler Beckett could have hoped for. He didn't even need to give the order, the naval officers would have given it for him when seeing him incapacitated like that. They were handed that fight on a silver platter. How did they possibly lose that?

Additional Note: The Endeavour which has 108 guns would have been a 1st rate ship of the line, this ship (comparable ship would be HMS Victory) would have been a lot bigger than both the Black Pearl and the Flying Dutchman combined with the supervisor armour thickness and firepower would have made this a non-contest, magic aside.

http://pirates.wikia.com/wiki/Black_Pearl http://pirates.wikia.com/wiki/HMS_Endeavour

I don't know why Lord Beckett didn't give out the order's but he's realized that there was nothing he could do about it. The chapter number is 25 "Good Business". Lord Beckett was trying to kill Jack Sparrow but it turns out Lord Beckett was wrong. I've seen this movie a million times (more than a million) and I still don't get why Lord Beckett didn't give out the orders to attack. I thought that was really really dumb of Lord Beckett, but hey, as I said before, Lord Beckett realized there was nothing he could actually do about it so he let his death take over for itself.

This kind of behavior has been shown on screen a few other times also. When a captain realizes that his death is upon him and that there's nothing he can do about it, they tend to shut down and forget about anything else. A couple of other examples off the top of my head: The Fifth Element (at the beginning, when a captain tries firing missiles at the source of evil that threatens Earth), Star Trek VI (Chang's cloaked ship about to be exposed) & Titanic (the captain shutting himself in the control room as the ship goes down).

Well I think differently.. What I believe is that Lord Beckett honoured his deal with Captain Jack Sparrow shown earlier in the movie. The deal was that if Jack leads Beckett to the meeting place of pirates, then Jeck was to go free without getting harmed. So Beckett honoured that deal, saying that its just good business, which according to me, means that all actions of Backett has only resulted in just good business for the company, nothing more. So then he had a change of heart and decided to keep his word he gave to Jack Sparrow. And when Beckett is faced with two ships, one is Black Pearl and other is Flying Dutchman, it is pretty obvious that Beckett couldn't order to attack any of the ships, because one has Jack Sparrow on board, and other is the Flying Dutchman which can not be sunk.. Pretty clear I guess..

I think it was because of Elizabeth

Earlier in the movie when Beckett and Sparrow were making a deal of their own in the movie, Beckett asks what will happen to Elizabeth, to which Jack responds by asking why he's interested in her. Despite everything he had done to her, he still believed he would have her as his own, since he believes he can have everything as long as he works for it and kills the right people at the right time.

When the Dutchman resurfaces though, Beckett finds out that Will is its captain, since Elizabeth quickly realized the same thing even though she was on a completely different ship, like Beckett. Since Will is the captain of the Dutchman, by default making him immortal, he also is now outside of Beckett's control unlike Davy Jones. Beckett also knows very well that Elizabeth and Will are in love, and that Will is immortal now, meaning that Beckett has now lost control over the Dutchman, which he thought was still under his control when it resurfaces, and control over Elizabeth, who he wanted to be with.

As minor as those things sound, the fact that Beckett finally cannot get something he has wanted shakes him to his core, since he has always gotten what he wanted no matter what. While he could have shaken off this shock sooner or later, it came at the absolute worst possible time when two very powerful ships were bearing down on him. He froze up, and because every decision runs through him first, the order could not be given when it could have easily been given, and so Beckett and his ship were obliterated.

Becket didn't give orders to fire because he instantly realized what happened - that Davy Johns was gone and that it was done by the reason of William Turner being killed and revived as a new captain of a Dutchman (he knew well what was the only way it could happen), and that William's and Elisabeth's love have won over all odds, - destiny itself being against their foes, - and that this power of love was the ultimate force in the Universe and it made Dutchman and Pearl come as one to attack the West Indie's fleet with total disregard about their lives. Because he was stunned by the power of this love, he felt that he can not go against it and destroy it with his canons any more. He suddenly become a man of heart. This can be even specifically seen on his facial expression at that moment - that he was deeply touched and stunned by that sacrificial love between William and Elisabeth and also readiness of their crew members to fight with them till the end. That's why he decided not to act but give in. And that's also why he said it was "a good business". That's the only secret about it, kids.

Nicely explained..George...I also think that Lord Cutler, irrespective of the overwhelming odds he faced, realized that this battle could no longer be won by sheer force and their love (Will and Elizabeth) has simply overpowered the situation. So he deciedes to choose rationally than logically and gives in thus respecting his agreement with Jack and dying a changed man who respected the will-power of those he faced against.