I have an Oster DLC-7 food processor. It has always been very hard to close requiring force. The last time I used it, a white plastic part popped off from the back. I don't know whether anything is broken or not, but I can no longer close it, and of course, it no longer works. I have the part and it doesn't appear to be broken. It is about 1 and 3/4 inches long with a sort of hook on one side and a **** that looks possibly like it sllips over something on the other side. It is about 1/2 inch wide. What do I do now?

You have a broken the door latch.Most people have the habit of slamming the door shut ( the same way some people hit the enter button on the computer ).With age the plastic becomes brittle and the slamming accelerates its demise. Now connected to this latch is a safety feature which shuts down the Microwave when the door is opened during cooking. So till you replace this latch the microwave will not work. Disconnect the microwave from the power outlet and remove the top cover ( 4 to 5 screws at the back ) , look near the bottom close to the DOOR OPEN button.You will see the rest of the latch with a spring attached to it.Do not attempt to glue the broken piece because the force exerted on the latch is very high and will not hold. You challenge is getting a replacement. Best would be to contact the seller or locate a authorized service center from where you might be able to procure it. It should cost you about 5$.