I recommend Fast Stone Capture, it has several capturing options, like full screen, full window (only the window you choose, even if it is not fullscreeen), rectangular region (which is what you want), and even freehand region and scrolling window, which is my favorite one, it can automatically capture any scrolling window in most programs, even if it has both vertical and horizontal scroll. That is specially useful for web pages or dialog windows. Other tools don't have that option and you would have to take several screenshots and then "paste" them together by yourself.
Also, you can trigger the capture via a small floating window, or via configurable keyboard shortcuts, and also you can copy the image directly to the clipboard, or to a (very nice) built in editor, or directly to a file, either asking for a name, or automatically naming it with several options like date, time, etc.
The current version is paid, but several versions before, it was completely free, so you can look for the last freeware version (it was version 5.3) and use it without any problem, it works pretty good! Of course the newer paid updates have other nice features, so its your call. Or i guess you can try the newer version for a trial period (not sure). Just check their site for more info.
Hope it helps!