My version of Microsoft Word 2013 came with Segoe UI Light, but when I go into my fonts folder, it cannot be found. I'd like to use the font in other programs including Windows and Sony Vegas, but it can't be found. It costs something like $35 to purchase, but I'm pretty sure it's somewhere on my computer if Microsoft Word can use it. What should I do?

You should do a Windows search of your C: Drive, for both .ttf and .otf - be sure to include the period, so the search will be for file type, rather than name. You'll be able to see the folder address in the results. If it's not currently in your fonts folder, copy/ paste a copy into fonts. Don't cut/paste, however, because it's probably supposed to be where it is now. Keep in mind that the search results will show the file names of the fonts, rather than the internal font names. for example, the font named Century Schoolbook Italic has file name SCHLBKI.TTF