If the microwave is still heating, but the carousel is not turning, this problem is commonly attributed to a turntable motor that has worn out and needs to be replaced. The following link explains how to access and replace one:
http://www.fixya.com/support/r3555716-replacing_a_turntable_motor_on_a_microwaThis is a very simple repair, that usually is not expensive. The price range will be determined by the model and manufacturer. This repair can also be performed on an over the range model microwave oven WITHOUT uninstalling it.
You can refer to any of the following websites for comparison:
searspartsdirect.com
pcappliancerepair.com
appliancepartspros.com
repairclinic.com
The first three sites listed offer helpful exploded view diagrams to assist you with locating and proprly identifying the part(s) you need.
If you have any questions, please post back with your and let me know. I hope this helps you.
NOTE: To answer your intial question, YES you can still use the microwave oven, but it is recommended that you stop the oven about midway through the cooking process and rotate your food to ensure it is heated evenly. Early model microwave ovens did not have a rotating carousel and it was often listed in the cooking directions to rotate your food this way.