Windows will not let you change the default open-with program on several types of files, including those with no extension and LNK(shortcut) types. This "file" you are trying to open appears to be one or the other. You could, in theory, get into the registry to change the association for LNK files, but good luck using any shortcuts after that. FWIW, LNK file extensions are "super-hidden" but you can see the extension if you go to a command prompt:
Winkey+R or Start > Run
cmd.exe (should open command window)
CD %userprofile%\desktop
DIR *.*
Your other question contains a comment that explains how to examine the association with .LNK files; you will need to follow -those- instructions, or edit the registry, to fix your shortcut issue.
Please note that shortcuts aren't actually the installed programs; they are pointers to the actual program you want to run. As such, you can run anything on your system directly, without needing the shortcuts, but they are convenient.
See this image :
as shown in image, I am unable to launch .lnk(any_program_shortcut.lnk) program. And .lnk has no option of "Change". and selecting .exe file each time is painful! so constructive solution will be appreciated... – Christopher – 2014-04-26T15:00:46.880