I think you probably want to look at POSIX (for strftime) and Time::Local qw(timelocal) as I discovered a year or so ago in Fast date parsing — although, for totally different reasons.

Without being able to use Date::Manip or Date::Calc (why again?) — I would personally probalby convert the dates to epoch seconds (strftime's %s) and subtract those. It'd be a bit more reliable than subtracting ... er, the mess you're subtracting.