If it can run Vista...... it can run Windows 7. As long as it is a legal copy of Windows 7 with it's own license key, it should activate fine after installation. Do you know if you have an upgrade version or a full retail version?
The upgrade version requires a valid copy of Vista installed. Once your start the installation process, you can choose if you want to simply update the current version of Vista to Windows 7 (this will keep all your installed programs etc) or if you want to do a clean install (which I would recommend, but you'll have to install all your programs and drivers after the windows installation).
And just out of curiosity......
What kind of computer is an HP E6-400?
I couldn't find it on the HP website.
Did you mean a Dell E6400?