Right now when I click the maximize button, it only goes about 1/2 of the screen, but I was wondering if there's any way to completely maximize the terminal window?
You can't, as that window isn't part of Cygwin, but a regular cmd.exe window (easily seen by right-clicking on the title bar and then selecting Properties).
If you want full-screen, set the buffer size of the command window to something large, which will always be in effect, even if the effective size isn't enough, or install the Cygwin/X parts (xinit and xorg-server should pull all the required dependencies) and run a regular xterm.
Cool, thanks! I didn't even think to check the Properties... 
I changed the Window Size, and it all worked out.