Given that you’ve got an external monitor that shows a display OK when connected to the laptop, most probably the motherboard is OK. Also seeing a white screen on the laptop screen means that there is probably nothing wrong with the backlight power supply either.
That leaves just the LVDS cable or the display panel.
Search online for HP (insert exact model number) service manual and when you have it use it to find out the necessary pre-requisite steps and then the procedure to remove /replace the display unit. This procedure will let you get access to the LVDS cable so that you can view its’ connections to the motherboard and the panel to see if they are OK. It will also let you check if the cable is damaged where it passes through the hinge to get to the panel.
If the cable and its’ connections seem OK then you’ll have to decide whether to replace the cable or the screen to determine where the problem is.
The part numbers for the replacement parts should also be available in the manual.
Once you have the part number, search online using the part number only in the search term of your browser, to get results for suppliers of the part.