It could be the sequence. Word 2007 and above made the Alt key a special trigger.

Try holding down the Ctrl key with one hand and pressing Alt+M with the other.

If that doesn't work, try (as a diagnostic, not a cure) starting Word in Safe mode. If there is the same problem, try starting Windows in Safe mode. If either of those allows you to use the shortcut, write back with what you did and the results. Someone can help you figure out where the problem is.