Oops, I hadn't noticed you had use DBI; inside the if.

use ...; occurs at *compile* time and unconditionally. In other words, your code is identical to

#!/usr/bin/perl
use strict;
use DBI;
my $use_dbi = 1;
eval("use DBI;");
$use_dbi = 0 if (not($@));

print `uname -n`;

print `prtconf |grep Mem` if (`uname` eq 'SunOS');
print `cat /proc/meminfo` if (`uname` eq 'Linux');

if ($use_dbi)
 {
  print "Hurray!!\n"; 
 }
else
 {
  print "NO DBI\n";
 }
[download]

It's quite easy to fix: Remove the use DBI; since it's already done in the eval EXPR. As you can see in my earlier fixed code, I removed that line (apparently without realising it!).

Here's the fix with a couple of small cleanups:

#!/usr/bin/perl

use strict;
use warnings;                      # Always good to have.

print `uname -n`;

my $uname = `uname`;               # Only run "uname" once.
print `prtconf |grep Mem` if ($uname eq 'SunOS');
print `cat /proc/meminfo` if ($uname eq 'Linux');

my $use_dbi = eval("use DBI; 1");  # More concise than checking $@.
if ($use_dbi)
 {
  print "Hurray!!\n"; 
 }
else
 {
  print "NO DBI\n";
 }
[download]