Detergent door wont close, buzzes when pushed close, wont latch

SOURCE: GE DW beeps and won't start

look for parts for the unit. you indicate its defective. if you can't replace the parts yourself, then you will need to get a repairman in for that.
be careful regarding the cost. some home repairs cost more than a new unit, so if its a base level unit (low cost) you might want to consider a new unit. you can also save money by taking the unit in to the service center. call first and work out a deal in advance. this only makes sense if you have a lot of free time and do not value you time very much.
good luck
mark

SOURCE: soap door latch won't latch close

Make sure the dial that you turn to start the dishwasher is all the way to the beginning. Sometimes my little grandson comes by and plays with it, turning it. I load, add soap and the dispenser won't close. I check the outside dial, and sure enough, set it to the very beginning and the dispenser locks in place!

SOURCE: Inside detergent compartment door will not open during cycle

to much detergent clean it out and start over

SOURCE: Detergent Latch - Not Locking

I have the same model in my apartment, did you make sure the outside dial is set to the "off" position?
If not, I know for sure you can turn the detergent door as much as you want and it will not lock shut, but if/when it's in the off position, it will.

BTW - one of the worst dishwashers I've ever seen, but if I didn't have it, my dishes would NEVER get done lol

SOURCE: I need to replace the detergent dispenser latch on

To replace the parts you have to buy a whole dispenser assemble for $100 to $200. To buy some time ... Get a heavy gage sewing needle - hold it with pliers and heat it red hot. Stick the hot end into the plastic door at the area where the plastic latch is (where it will line up with the far end of the latch mechanism). when it cools cut off most of the needle leaving one eight to one sixteenth (more or less) protruding. Use a drill and small bit to remove some plastic (or drill a small hole) on the spring latch mechanism. push the remaining part of the needle in or out to engage the hole in the latch.. this will hold awhile.