Often when this happens to me, I find haven't actually successfully copied the piece I thought I had, and a second go works just fine. If you are using CONTROL + C or CONTROL + X to copy or cut, try instead right mouse clicking and select from the dropdown instead; that way you have visual confirmation you struck the correct command.

You can also see what's going on by looking at the Clipboard. I believe in 2007 you can still operate a classic menu keyboard or the newer ribbon one. If you don't know where it is, check out this for visuals:

Where is the Office Clipboard in Microsoft Word 2007, 2010, 2013, 2016, 2019 and 365

The clipboard will likely hang onto the last thing you cut or copied until replaced by something new. Thus, if it flubbed the new cut or copy, you could paste the most recent thing.

With the clipboard displaying on the side, do your copy again and you'll see whether it's been added to the clipboard for subsequent pasting. If you keep trying to copy and nothing happens, make sure that the file you're copying from is not locked or protected against it. In Excel, sometimes I miss the little button at the top that calls out that it's in Protected View, and I have to enable editing, which includes copying out contents.

Sorry, I'm a little rusty on Word 2007, so if I am incorrect that these features are even applicable in your version, I blame the passage of time.

- Ann