Video Cable may be damaged, causing the display to quit. Video Cable shorting out.
Remove ALL power. Remove the AC adapter (Charger), and Battery.
Page 70. (Adobe Reader page number box at top)
Remove all components down to the Top Cover. (Palm Rest Cover)
Page 71. Disconnect the Video Cable.
(Display Panel Cable, and Number 1 in the figure photo)
Let's see if you still have a problem with the external display.
HP Support > HP G72-227WM Notebook PC > Main Support page > Manuals,http://h10025.www1.hp.com/ewfrf/wc/manualCategory?cc=us&dlc=en&lc=en&product=4290949&
In the list click on -
Compaq Presario CQ72 Notebook PC and HP G72 Notebook PC - Maintenance and Service Guide
This is a PDF file. The computer you are using now has Adobe Reader on it, which uses PDF files.
After you click on the above file name it may take up to 30 seconds, before the first page comes up.
(Using medium speed DSL connection. Took 6 seconds just now)
ONCE the Top Cover is removed the STATIC shock sensitive components are exposed.
Your body carries Static electricity. Static WILL fry out, (Short Circuit), the delicate hardware components inside a computer.
(Laptop or desktop)
A Processor is the MOST susceptible hardware component to Static shock.
For this reason it would be a GOOD suggestion for you to wear an ESD wrist strap, and have it's alligator clip attached to a good ground source, BEFORE removing the Top Cover.
Average price is around $3 to $6. Here is but one example,http://www.radioshack.com/product/index.jsp?productId=2103245
I connect to an unpainted surface, of the metal frame of an open, empty desktop computer case.
(I feel an Anti-Static mat is unwarranted)
You can also set a large metal serving tray (Unpainted), on the table you're working on, and connect to it.
Or a large metal knickknack. (Unpainted)
Post your results in a Comment.