How can I fix this broken cupboard?

Is it in the kitchen? Paint inside and put a covered waste can there, or a wicker hamper or get someone to make you a new door and you can pull the unit together more...for the side,, cover it with thin wood and paint it with chalk board paint.

You put some shelves in it with a few baskets for storage.

You can make a waste area : cut a pannel from dimention of the missing door, put some piano hinge at the base, a chain to retain it at the top, and a handle, and à square metal frame from dimension of the inside space to carry the waste bag open. You will mask your waist bin like this...

IF there is a door from another cabinet that will fit, move it to close the bottom. Now you have an open cabinet space at eye level. Add shelves to hold pretty things...like folded towels, books, fake seasonal flowers, plates & glasses, etc.

To hide the ugly end side, add interesting hooks to hang pretty things...like towels, an apron, etc. Or add a framed corkboard or chalkboard for a message center. Or make it an art gallery with framed family pictures.

Two ideas came to mind- Velcro pretty fabric as a curtain and paint the cabinets OR use self adhering wallpaper inside and paint outside-either way allows attractive use for storage without the door And might add character to your space as well as functionality. Here's an example of the wallpaper and paint on shelves I'm using.

Those appear to be standard size cabinets not custom so you can probably search out the same door in Home Depot, lowes or any cabinet shop. Take a door with you so they match. You can also keep checking at a Habitat store. People bring them in all the time so you might have to make a few trip. Craigslist in some cities wants people to remove cabinets for free or are selling some. I would try to match it first.

You can keep your laundry basket in there, you can try and gety a nice large woven basket..

Move the door to the bottom of the cabinet and continue with idea above! Shelves!