To get Serial and Product Number from command on Windows.
Go to > Start > Run type > cmd >
wmic bios get serialnumber
wmic csproduct get name, identifyingnumber

To get Serial from command in Ubuntu
#sudo dmidecode -s system-serial-number

To get Serial and Product Number from command in Linux(Redhat/CentOS/Fedora/SuSe)
#sudo dmidecode -t 1 | egrep -i "serial|product"

http://www.techgyaan.org/2011/10/how-to-find-serial-and-product-number-from-command-line-on-windows-linux-unix/

보증지원 확인
https://h20566.www2.hp.com/portal/site/hpsc/public/wc/home/