If you really can't use any modules, even a core one that ships with Perl itself (and you should ask why not, if that is the case), then simply scan over the @ARGV array and take appropriate actions, something like (untested):

for (my $i=; $i < @ARGV; $i++)) {
   if ($ARGV[$i] eq "-l") {
      warn "Logfile $ARGV[$i+1] missing\n" unless -e $ARGV[$i+1];
   }
   elsif ($ARGV[$i] eq "-u") {
      warn "Useraccounts $ARGV[$i+1] missing\n" unless -e $ARGV[$i+1];
   }
   else {
      warn "Invalid switch $ARGV[$i]\n";
   }
   $i++;
}
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