My Miele 1913W washing machines detergent drawer won’t open. How do I get it to open

SOURCE: Hoover Nextra washing machine - water backing up

If this is a front loader see that u use only washing powder for FRONT LOADING MACHINES. Also possible your detergent drawer is clogged with old dry detergent. Pull out the drawer and clean with tooth brush. Things shd be fine.

SOURCE: detergent dispenser stuck, I think the detergent cup is preventing the drawer from opening

Here there is a user guide and instructions of a similar washer model.
http://www.laundrymanuals.com/manuals/mfg/lg/wm2496h.html
and also all available LG washer manuals to download.
http://www.laundrymanuals.com/manuals/mfg/lg/lg_frontload_washer_product_list.html
Have a look of how top lid is mounted.

SOURCE: miele G660 premier dishwasher

There is a solenoid that opens the door to the dispenser. You can check it with a volt/ohm meter. Sometimes large dishes can block the door keeping it from opening. I personally know on some Whirlpool washers (because it was mine) that if the bottom drawer is put in backwards, it wont let the door open. When I opened the main door, then the dispenser would flop open. You need a meter to check this part if its not the other things. Without it, you are just guessing.

SOURCE: Detergent dispenser drawer stuck

You may have to remove the washer top (three phillips screws at the back, then push top back about two inches and lift it off) then drill a hole in the top of the plastic dispenser to allow you to use an object like a screwdriver to maneuver the offending part around so it will drop down and allow you to open the dispenser drawer. Use foil tape to seal hole if you don't want to buy a new dispenser. Clean out blue plastic dispenser parts so detergent will siphon out completely. Pushing down on the center tab at the back of the dispenser should allow you to take the dispenser drawer the remainder of the way out. In the future, make sure you do not use over 1 tablespoon of HE soap (and 1 teaspoon of fabric softner) max per load. Even less if you have 2x or more detergent.

SOURCE: Fabric conditioner drawer

Try cleaning inside the the machine where the soap dispenser drawer fits into. Sometimes this builds up with lots of soap and fabric conditioner residue and stops the conditioner from going through.
Take the drawer back out and look inside where it goes to see if there is a build up of soap etc...
hope this helps