Rajiv:
I just repaired an inverter for a 15" Viewsonic LCD. It was a dual
lamp one like yours. Two transistors that drive the transformer for
one of the lamps were bad. I used the diode position on my DMM to
check the SMD transistors. Replacing the transistors with regular
larger TO-92 case style ones fixed the problem.
I found that if you hold a small NE-2 bulb near the transformer, the
gas in the bulb will glow if there is high-voltage AC close to it.
If the bulb glows, the inverter for that section is working OK.

Most inverters will shut down if there are problems on the board.
The bulb would glow for just a second or two, then go out. It would
not glow near the transformer with the bad driver transistors.
The 4 wires going to the inverter on mine were
12 Volts, ground, enable, and dimming (some will change the voltage
on the lamps to control brightness).
It helps having a dual-bulb inverter in that you can check back and
forth between the parts on the two ends of the inverter board.
I have seen places on the Internet that sell the inverters for
between $70 and $130 (plus shipping).
Hope this helps...
John