Map Shift + F3 in .vimrc
Solution 1:
You're using Vim in the console, not GVIM, right? Anything other than the plain function keys is problematic, and best avoided; try using a prefix like <Leader> instead. If you really want this, you can try the instructions at http://vim.wikia.com/wiki/Mapping_fast_keycodes_in_terminal_Vim for getting function keys with modifiers to work.
Solution 2:
It should be <S-F3> not <SHIFT-F3>, see :help key-notation in Vim.