Content Delivery
In your cd_deployer_conf.xml, modify the "Cleanup" attribute of the Queue Location element to be "false":
<Queue>
<Location Path="c:\tridion\staging\incoming" WindowSize="20" Workers="10" Cleanup="false" Interval="2s"/>
</Queue>
Restart your deployer for these changes to take effect.
Content Manager
Modify your cd_transport_conf.xml, add a "Cleanup" attribute with the value of false to the Workfolder element:
<WorkFolder Location="./transactions" NotificationBatchSize="10" Cleanup="false"/>
The packages will appear in [TridionHome]\bin\transactions.
Restart the transport service for this change to take effect.
DO NOT FORGET TO CHANGE THIS BACK AFTER YOUR INVESTIGATION or face the wrath of some very annoyed users when your servers run out of disk space...