If the HP has Windows 7 Pro or Ultimate, it comes with Remote Desktop Server. Temporarily connect the HP to an external monitor to enable Remote Desktop Server.
https://technet.microsoft.com/en-us/magazine/ff404238.aspx
You can then disconnect the monitor. Start up Remote Desktop client on the Dell, and connect to the HP laptop's name. Enter your login and password, and you will see the HP's desktop on the Dell's screen.
If the HP doesn't have Pro or Ultimate, you can use VNC instead. VNC isn't as network-efficient as RDP in my experience, but it'll work just fine for mundane tasks (i.e. no video). Install a VNC server on the HP, and a VNC client on the Dell.
The quality of your experience will depend on your network...