Hello,
For the LCD screens. the best resolution is their native resolution, so 1680x1050 in your case. What are your system' specs? An old Pentium dual core with on-board video (HD4500) and 2GB of RAM should have no problems playing 720p videos. If you want to lower the screen resolution, at least use resolutions with close ratio as the native one: 1680x1050 has 16:10 screen ratio, so try to use 1440x900 or 1280x800.
Are you sure you have the proper GPU drivers installed?