After changing the display can you see it is working when lit with a flashlight ?
Yes : the backlight still isn't working.
What do you know about the exchanged parts ? Brand new or used ? Even new parts can not always be trusted to be all right. So it still could be the inverter, or the lamps in the display panel.
When these parts are brand new and tested, check the inverter supply (mostly 12VDC) voltage. Maybe there is a fuse on the power supply which has blown. Also check the low voltage wiring to the inverter. There can be a short circuit in the high voltage wires to the backlight lamps, causing the fuse on the new inverter to blow instantly. SMD fuses can be recognized by the desription on the PCB (F1 e.g.), and can easily be tested with a multimeter, and replaced by a glass fuse by soldering wores to it.
Then there is the baklight control voltage (mostly a PWM signal) coming from the motherboard to the inverter (sometimes passes the power supply PCB). It controls the brightness of the backlight and could be missing or too low. Then mostly there is a Backlight_ON/Inverter_ON signal which could be the cause.
The backlight lamps can not be tested with a multimeter (infinite resistance), and they normally break only because of over-aging (or by heavy mechanical shock).
When you can't see anything with a flashlight on the new TFT panel, it could be broken (even though it is new). Try testing the old TFT to see if that one is still displaying something (maybe by connecting the new TFT you broke the video card).
Please let me know about your own diagnosis and remedy.