Have a look at XML::LibXML::Iterator which, with a bit of trial and error, I got to produce your desired output:

use XML::LibXML;
use XML::LibXML::Iterator;

my $string = q|<?xml version="1.0"?>
<PARTS>
<TITLE>Computer Parts</TITLE>
....
</PARTS>|;

my $doc = XML::LibXML->new->parse_string( $string );
my $iterator = XML::LibXML::Iterator->new( $doc );
 
my ($path,$value) = ('','');

while ( $iterator->nextNode ) {
    if ($path and $value) {
        print "$path $value\n";
        ($path,$value) = ('','');
    }
    my $current = $iterator->current;
    my $type = $current->nodeType;
    if ( $type == XML_ELEMENT_NODE ) {
        $path = $current->nodePath;
    }
    elsif ( $type == XML_TEXT_NODE ) {
        my $text = $current->nodeValue;
        chomp $text;
        $value = $text if $text;
    }
}
[download]

Output:

/PARTS/TITLE Computer Parts
/PARTS/PART[1]/ITEM Motherboard
/PARTS/PART[1]/MANUFACTURER ASUS
/PARTS/PART[1]/MODEL P3B-F
/PARTS/PART[1]/COST  123.00
/PARTS/PART[2]/ITEM Video Card
/PARTS/PART[2]/MANUFACTURER ATI
/PARTS/PART[2]/MODEL All-in-Wonder Pro
/PARTS/PART[2]/COST  160.00
/PARTS/PART[3]/ITEM Sound Card
/PARTS/PART[3]/MANUFACTURER Creative Labs
/PARTS/PART[3]/MODEL Sound Blaster Live
/PARTS/PART[3]/COST  80.00
/PARTS/PART[4]/ITEM inch Monitor
/PARTS/PART[4]/MANUFACTURER LG Electronics
/PARTS/PART[4]/MODEL  995E
/PARTS/PART[4]/COST  290.00
[download]