"PC World/Parceline will be made to pay" is unfortunately not likely at all.
The goods are at PCWorld's risk until delivered, but they have no liability for your time, travel, or telephone calls. They would probably replace the goods on receipt of your evidence, but as you've done that yourself you're only option now is to cancel the order under the 7day supply of goods and services regulations. This has the effect of negating the contract completely, and PCW have 30 days to return your money. In practice that normally happens sooner, but the law allows them the 30 days. The regulations state that you must retain the goods pending further information from PCW about return, but of course in this case there are no goods to return.
To be fair, it isn't PC World's fault that someone opened the package in transit. Parceline have no obligation to you at all - their contract was with PCW, so you can make no claim against them.
"Check before you sign" is certainly very good advice, although most of us have probably forgotten it at some point.