There are 3 possible causes for blank LCD:
1 - the light source/inverter for LCD panel is bad
2 - LCD panel itself is defective
3 - graphics card went bad.
1 and 2 can be found out if you connect laptop to external monitor. It is the only way to find out. The tech support was correct in this. If the external monitor shows image, then the cause is option 1 or 2. Replacing backlight can be more affordable if you do yourself and has the skills (about $50 US). Replacing monitor is expensive, better to buy new laptop.
If no image on external monitor, then graphics card or motherboard (most likely) went bad. It is expensive to replace motherboard. Better to buy a new laptop.