You need to bear in mind that Luke attempts to open the door, and Han tries to blast it, but as soon as they get in, they don't really have time to ask C-3P0 to open the door because there entire episode in the masher is eventful.
I've left out any dialogue to keep it as concise as possible
Han tumbles into a large room filled with garbage and muck. Luke is already
stumbling around looking for an exit. He finds a small hatchway and struggles
to get it open. It won't budge.
Han draws his laser pistol and fires at the hatch. The laserbolt ricochets
wildly around the small metal room. Everyone dives for cover in the garbage as
the bolt explodes almost on top of them. Leia climbs out of the garbage with a
rather grim look on her face.
A loud, horrible, inhuman moan works its way up from the murky depths.
Chewbacca lets out a terrified howl and begins to back away. Han and Luke stand
fast with their laser pistols drawn.
Suddenly Luke is yanked under the garbage
Suddenly the walls of the garbage receptacle shudder and move in a couple of
inches. Then everything is deathly quiet... With a rush of bubbles and muck
Luke suddenly bobs to the surface.
Luke seems to be released by the thing.
Before anyone can say anything the walls begin to rumble and edge toward the
Luke pulls out his comlink.
Threepio! Come in Threepio!
Threepio! Where could he be?
INT. DEATH STAR - MAIN GANTRY - COMMAND OFFICE
A soft buzzer and the muted voice of Luke calling out for See-Threepio can be
heard on Threepio's hand comlink, which is sitting on the deserted computer
console. Artoo and Threepio are nowhere in sight.
A trooper pushes a button and the supply cabinet door slides open. See-Threepio
and Artoo-Detoo are inside. Artoo follows his bronze companion out into the
The troops hustle off down the hallway, leaving a guard to watch over the
Use the comlink? Oh, my! I forgot I turned it off!
A New Hope - Script
At this point the trash compactor is almost shut:
The walls are only feet apart... She's terrified and suddenly groans as she feels the first crushing pressure against her body.
So from the script we see that Luke never has time, as mentioned by Valorum, too look at the unit number on the hatch, because of the monster and crushing walls. And when they try to contact 3P0, he's stuck in hiding from the Empire, with the com-link on the table