|If you still have the original drive, it's...|
"Multimedia Drive - LightScribe Super Multi 8X DVD?R/RW with Double Layer Support"
This drive can burn and read both CDs and DVDs - it has at least two lasers and associated circuits - sometimes one of those burns out after the drive has been used a lot.
If the following doesn't help, you will have to replace the drive. You don't necessarily have to buy the same HP drive, or any HP drive - HP didn't actually make it in any case. There are lots of drives with the same specs or better specs available on the web for less money than HP wants. All that's required is they are compatible with being installed in your laptop model. Search for a replacement drive using your laptop model number on the web.
The laser lens may be too "dirty".
If you can see the laser lens on the drive tray when you eject it when there is no disk on it, try cleaning off the laser lens with a tissue or cloth.
If you can't see the laser lens, use a laser lens cleaning CD in the drive. If you don't have one, most places that sell CDs and DVDs and places that sell lots of stuff for computers have that, or even some "dollar" stores have that for a buck or two.
The drive must be able to read the type of DVD you have inserted. E.g. if it's a DVD-Ram disk, not all DVD drives
can read them.
If the DVD is a burned disk with data on it, the DVD drive should read any DVD-R (or CD-R) properly, but it may not read another type of burnable disk properly unless it was made in the same drive.
All optical drives are somewhat sensitive regarding which media - brands and types of burnable disks - you can use in them. It may not be able to read all burnable disks properly that you try with it.
Go to Device Manager.
RIGHT click on My Computer, select Properties - Hardware - Device Manager
Is the DVD drive listed under DVD/CD-Rom drives?
If it is, is the list expanded and has a yellow ! or a red X beside the drive?
If yes, did you install more than one add on burning program on the laptop?