Unfortunately there is no free upgrade from Vista to Windows 7. The only time that was available was near Vista's end of life. If you purchased a new computer HP would send a Windows 7 disk.
The other possible problem is if there are Windows 7 drivers for your computer and other devices such as printers. Usually a Vista driver will work on Windows 7.
The cheapest way would be to purchase a Windows 7 OEM license.
Edit:Because you have another computer with Windows you may want to think about putting a linux distro like Mint or Ubuntu on the computer.
What are the specs of the computer? I could not find anything on that model number.
Edited by JohnC_21, 01 February 2016 - 07:30 PM.