It works perfectly for me:

use strict;

my $source = 'VM';
my $COB    = '20080605';

while (<DATA>) {
    if (/^$source.*$COB/) {
        print "Matched $_";
    } ## end if (/^$source.*$COB/)
} ## end while (<DATA>)

__DATA__
VMTKSWPDCN0120080717.TXT
VMTKSWPSLN0120080717.TXT
VMTKSWPDLA0120080717.TXT
CMVMCSHFEN0120080605.TXT
VMTKSWPDLN0120080605.TXT
VMTKSWPTVN0120080605.TXT
VMTKSWPSLN0120080605.TXT
VMTKSWPDLA0120080605.TXT
VMTKSWPTVA0120080605.TXT
VMTKSWPDCN0120080605.TXT
VMTKSWPSLA0120080605.TXT
[download]

Output:

Matched VMTKSWPDLN0120080605.TXT
Matched VMTKSWPTVN0120080605.TXT
Matched VMTKSWPSLN0120080605.TXT
Matched VMTKSWPDLA0120080605.TXT
Matched VMTKSWPTVA0120080605.TXT
Matched VMTKSWPDCN0120080605.TXT
Matched VMTKSWPSLA0120080605.TXT
[download]

Are you sure that $_ contains the correct string to match?

Note: if you have to match against a huge number of strings, it will be faster to pre-compile the regex-pattern:

my $source = 'VM';
my $COB    = '20080605';
my $regex = qr /^$source.*$COB/;
while (<DATA>) {
    if (/$regex/) {
        print "Matched $_";
    } 
}
[download]