And here's one more (perhaps "ugly" :) option:

use strict;
use warnings;

my @col1 = split ' ', <DATA>;
<DATA>;
my @rows = map { my @row = split; \@row } <DATA>;

my $i = 2;
for my $col (@col1) {
    print "$col\t$_->[0]\t$_->[1]\t$_->[$i]\n" for @rows;
    $i++;
}

__DATA__
               A     C     F
SampleID        Time    ObsConc ObsConc ObsConc
5        24      2.27E+06        687.02  32521.94
5        168     1.92E+06        525.02  22198.44
5        12      2.94E+06        896.39  41331.61
5        -0.5    2.23E+06        942.34  40616.49
5        8       4.03E+06        1371.32 45863.69
6        24      1.02E+06        1057.89 46341.04
6        168     3.14E+06        4987.32 42166.08
[download]

Output:

A    5    24        2.27E+06
A    5    168        1.92E+06
A    5    12        2.94E+06
A    5    -0.5        2.23E+06
A    5    8        4.03E+06
A    6    24        1.02E+06
A    6    168        3.14E+06
C    5    24        687.02
C    5    168        525.02
C    5    12        896.39
C    5    -0.5        942.34
C    5    8        1371.32
C    6    24        1057.89
C    6    168        4987.32
F    5    24        32521.94
F    5    168        22198.44
F    5    12        41331.61
F    5    -0.5        40616.49
F    5    8        45863.69
F    6    24        46341.04
F    6    168        42166.08
[download]

Hope this helps!

Edit: My thanks to poj for pointing out that my script didn't properly generate the last column's values. This is fixed.