The cover for the oven light has broke leaving the screw part inside cannot get it out.

Changing the light bulb on your Sharp carousel microwave will allow you to have needed light inside the oven. Microwaves are not designed for consumers to change the light bulb due to manufacturer liability, but it can be done. Following the proper steps will ensure a successful installation. Step 1 Unplug the Sharp carousel microwave from the electrical outlet.
Step 2 Locate the screws around the outer cover of the Sharp carousel microwave and unscrew all the screws.
Step 3 Lift off the covering.
Step 4 Locate the bulb and unscrew. Screw in your new bulb.
Step 5 Replace the cover and screw back tightly. Once done, test your new bulb.

The cooktop light bulb(s) is(are) located on the underside of the microwave oven, and is(are) replaceable. Remove bulb cover screw, and open the bulb cover. Replace bulb, close bulb cover, and secure with screw. Cavity light: The cavity light bulb is located behind the vent grille at the top front of the microwave oven, under the bulb cover, and is replaceable. Remove 2 screws on the vent grille, tilt the grille forward, and lift it out. Open bulb cover and replace bulb. Close bulb cover, replace vent grille, and secure with screws.
For more information, your owners manual can be viewed here (scroll to the bottom of page 4):
Maytag MMV1164WB Owners Manual Page 4

If it is at all like a plain microwave oven, you will have to remove the screw for the cover to access the insides and likely will find that the light is not a simple screw-in bulb but a sealed package with a spare of spade terminals on top. It may be held in by one or more screws.
It is possible that this could be like a new conventional oven where you have to remove a light cover inside the cavity to access the bulb and change it

My Spacesaver bulb replaces from the top. You have to remove 2 screws that hold the upper vent cover. W/ cover off you will find a phillips head screw about the center that holds the bulb cover. Remove the cover screw & lift up & remove the cover, then replace the bulb, the cover & screw then put the vent cover & it's 2 screws back. There may be some variance but they are all similar.

If your waveguide cover is damaged, it will need to be replaced.

It provides critical protection for the magnetron and waveguide.

The inside light (unlike the cooktop lights) is not meant to be user replaceable.

You have to remove the oven from the wall, remove the outside cover, then you'll see the lamp on the right side of the oven in its socket on the air duct near the magnetron.

The installation instructions make this much easier. If you don't still have yours, we have those form a similar model here to help you. I hope they're close enough.

We have the service / repair manual for this model and have uploaded it to our site here for free download to help you.

You can order Sharp parts from the Sears Parts Direct Web site or from Encompass here.

We're happy to help you with free advice and we'd appreciate your thoughtful rating of our answer.

The back of the door will have a moulded surround that will be fixed with allen heads or small screws. Remove the inside cover of the door and you will see the holes for the handle.

Just gone through it myself. Wife was trying to change the bulbs and broke them both leaving the screw part stuck inside. I took the whole bottom panel off. It is 5 screws and comes completely off the microwave. Makes things much easier access

hi my name is mark, you will need to remove the cover to get to the door switch. #1 unplug microwave leave unpluged for 10 minutes or more. remove cover. find a piece of card board from the back of a paper writing tablet say 2'x3' you use that as a gauge. close the door on the card. loosen screws that hold door switch and adjust switch assembly so all the microswitches are closed, reinstall cover but dont put the screws in plug in oven and check operation. if oven works install screws. if not there might be other problems. make sure you unplug the oven for 10 minutes or more before removing cover. hope this helps. thanks for your question.

Yes it can.

SAME PROBLEM FOR ME...I REMOVED THE BOTTOM COVER AND FOUND THAT ONE LIGHT WAS NOT FIXED AND WAS LOOSE AND WAS TOUCHING THE GLASS. THIS HEAT WAS WHAT BROKE THE GLASS COVER. CLOSED INSPECTION SHOWED THE LIGHT SOCKET WAS TOO LARGE FOR THE CLIPS AND WERE NOT SECURED WHEN PURCHASED. I GOT SMALL SCREW AND NUT, BENT CLIPS SO THE SOCKET HOLE MATCHED THE HOLE MADE BY THE CLIP AND SECURELY ATTACHED THE SOCKET. THIS WILL SECURE THE LIGHT AND KEEP IT FROM TOUCHING THE GLASS..........IF I CAN EVER FIND A GLASS REPLACEMENT....MAY JUST HAVE ONE CUT. NOW THE PROBLEM IS TO REPLACE THE LIGHT AND MICROWAVE FUSE WHICH WAS BLOWN WHEN THE GLASS BROKE.