|"hp Mini 1000" isn't specific enough.|
Scroll down a bit.
Look for the similar label on the outside of your computer.
Quote the specific model number - that's at the end of the first line.
Quote the Product number - that's on the third line.
"Yes unfortunately the HP mini was dropped... the dropping resulted in a bent/broken AC adapter and this problem of the screen not turning on."
The first two categories I listed are the most common reasons a technician who posted on this site says require that major components inside the laptop or netbook need to be replaced.
It may cost more to replace damaged components that this netbook is worth, even if you replace them yourself with the help of an available Maintenance manual.
The hard drive is probably okay, and you could connect it to another computer and get your personal data off of it.
"...instead of a VGA jack onboard, a HP mini expansion port instead."
The owners manual for a HP Mini 1000 model l randomly picked has an "Expansion port " on the left side that "Connects an optional VGA cable, which allows you to connect an external VGA monitor or projector" .
It would probably have cost you less to order that.
"I have bought a USB to VGA jack to test this"
What do you mean by that ?
It would have to be a USB video adapter, not just a USB to VGA jack.