My daughter has a Pavilion dv4-1220 at school and called that her screen went out. The tech guy at the university told her that repairs would probably be more than a new one would cost and that a monitor connection went out and it is past the 1 year warranty. What is the best action in this case, finals are in 1 week. Does this happen often?

This is one of those 'it depends' things. Usually what fails is the backlighting system. A lcd screen works sort of like a projector. IT requires a backlight shinging through it to be able to see the images. If you (or your daughter) looks at the screen with the laptop running you may see a very ghost like image of the normal desktop display. If that is the case then your display is fine it is jsut the backlight. That can be fixed for about $100.

Since you won't have time to fix it the next thing to try is hook up an external monitor to the laptop. If that works then we have both confirmed that the backlight is the problem and more importantly you can use the laptop as sort of a desktop until you either replace or repair it. It also will let you save off all of her documents and important files before you send it in or replace.

If the external monitor does not work then the chances are the video section has failed. That requires that the mainboard be replaced that is worth about $299 for that model (plus labor and shipping). Not all is lost as you can take the drive out of the laptop put it in a external usb drive enclosure and read the files using a differant computer.

It may be past the 1 year warrenty for HP but is there other warrenty such as store? If you purchased from a chain store they usually try to sell you a store extended warrenty. This won't help you get it fixed that fast but after it at least would pay for repairs.

The most imminent solution regarding her finishing her work (apart from buying a new laptop) is to connect the PC to an external screen through the VGA-connection or even a TV through the HDMI-port.
Although I would like to get a more detailed description of the damaged screen and the symptoms, in order to make sure there is no other viable option.
Worst case scenario would be to buy a new laptop and then transfer the data from the old onto the new one. This might require some technical skills though, but if she's friendly with the tech-guy at school, then that would probably do.