Use Dell Inspiron laptop monitor as only monitor for mac mini
You cannot connect the Dell laptop's screen to the Mac Mini.  Not easily anyway.  I am sure somebody could hack something together, and it would involve opening up the case of the Dell, and possibly the Mac.

However, you could use VNC on the Dell, to view what the Mac Mini is "displaying" 

I don't think you can use the Kick Start utility to start the screen sharing service on the Mac Mini, so you will need to borrow a monitor form somewhere to get the Mac set up in the first place... 

Then, after setting up the Mac, go to System Preferences -> Sharing, and set up Screen Sharing.  Also you will need to allow computers using VNC to connect to it.  It's all there is the settings pane.

Then...  You will use VNC on your ubuntu box (ick, don't use Windows) and connect to the Mac using it's IP address.  You will be able to view and control the mac, from the Dell's monitor, Keyboard, and Mouse.

There will be some lag...  such is life with VNC...