You can use Windows Remote Desktop or VNC to project the Dell's desktop onto the HP's screen via your network.
However, unless you have some other means of temporarily viewing the Dell's desktop (like an external monitor), it's going to be very different or impossible to configure Windows on the Dell correctly so you can use either of these. And if you can plug in an external monitor to use the Dell, you might as well just do that instead of messing with Remote Desktop or VNC.
You aren't going to be able to use the display on the unbroken laptop as a monitor for your laptop with the broken screen to the best of my knowledge. Laptops don't generally have video inputs, only outputs. A few older Alienware laptops are the only exceptions to this rule (that I know of).