To start, remove the battery, disconnect the power adapter and hold down the power button for 30 seconds to discharge the capacitors and clear BIOS memory. Reconnect power. Hold the D button down and press power at the same time. This runs a self test on the LCD panel. Does anything come on the screen? It should show coloured lines.
If, after connecting an external monitor, you find that the computer is working but the display still doesn't come on and the LCD self test didn't work the problem is with the LCD or the cable or connections.
If the display does work now, try replacing the CMOS battery on the bottom of the system board.
If you have no output to the monitor and the LCD test doesn't work your motherboard is faulty. It's likely the GPU that's at fault. You can try reflowing it if you have a hot air soldering station (this is what I'm thinking your tech did) but it will only last a short time. You could reball it if you have access to a BGA rework station, but if you do I'd suggest replacing the GPU IC altogether with a new one.
If you do reflow or reball make sure you get some GOOD thermal paste to put between the GPU and the heatsink to help protect it. This laptop has a lot of heat related problems.