First, you probably don't have 16W of light, more than likely you have 36W. You said you're lights were 60cm, and since most light fixtures arrange their lights parallel to each other and not end to end, you've got two of the 600mm lights, not two of the 300mm lights, right?
Second, before you start going out and buying a lot of stuff, you have nothing but Java fern in that tank, which would do fine even if you do have only 16W of light. If you plan on getting some more demanding plants in the future, then by all means do your upgrades, but I don't believe you need anything more for it than what you're providing. You can grow Java fern in a bucket in your basement.
The problem you're having is more than likely the plant getting acclimated to it's new surroundings. Some Java ferns do this when the conditions they are introduced to are greatly different from the ones they were used to. It doesn't happen too quickly because these guys don't grow quickly. Just trim off the dead leaves and be patient. New growth should appear that's more acclimated to your tank.
