Getting the serial number is one of those regular things you will need to do when you call HP. What you will find with the 3 Par is that it has 2 serial numbers. A 3Par and HP Serial number.
The 3Par serial number is easy to find. As soon as you log in to the GUI you will be taken to the dashboard view and you will see it here as the third item down on the right, shown in the screenshot below. You can also show the 3Par serial number from the command line with a showsys.
When you call support they always seem to need to convert the 3Par Serial number into a HP one and then log the case. So to save time you can get the HP serial number by running from the CLI shownode -i –svc, under the nodes section of the output you will see the HP serial numbers listed as scalable serial.