First, note that the “combining” code numbers have to be typed from the numeric keypad.
But you might not have to use these combining code numbers. Many fonts natively include glyphs for such accented characters. For example, Palatino Linotype includes glyphs for LATIN CAPITAL LETTER W WITH CIRCUMFLEX, and LATIN SMALL LETTER W WITH CIRCUMFLEX. The corresponding Unicode HTML entities are 372 and 373, respectively. So if you are typing Palatino Linotype characters, and you want to insert w with ^, you need to type ALT+373. This is working in Word 2007. Same thing with Calibri, Arial, Times New Roman, Lucida Console, Georgia, Verdana, and most common fonts.
Whenever you want to find the codes for such accented characters, go to
Unicode Character Finder, and enter the type of accent you need in the “Search character descriptions” box. If, for example, you enter “CIRCUMFLEX”, you’ll get something like the attached screen capture. You can then take your pick from the drop-down list.