Look on the power supply board itself, there may be a very small capactior, like a 1 uf maybe about 3-4mm in diameter, replace it or all the 1uf you can find, they are cheap. Get the 105c rated ones at 35 or 50V
Due to still having a power light you can bet the power supply is still fine.
The problem will be in the inverter circuit, but more to the point it's actualy one of the CCFL tubes that has blown.
They can be easy to replace, they can also be a complete nightmare.
Hope that helps =)
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