Your problem is that vim does not know what does terminal emit when you press <F2>. On some terminals it emits something like <Esc>[12~, so the vim quits current mode (or just beeps if it can’t) (<ESC>), does nothing ([1: there must be some key after [, but not 1, so it does nothing) and changes case of two letters (2~). So, you should open .vimrc and write there the following:
set <F2>=<C-v><F2>
where <C-v><F2> means that you must press <C-v> and then <F2>. This line should tell the Vim the exact sequence of codes which is emitted by terminal when you press <F2>. After that, use noremap <F2> whatever and it should work. If it is not the only terminal that you are using, then you may want to put if $TERM==#"<C-r>=$TERM<CR>" before this line and endif after.