I think we need more parameters.
Your initial parameter of "dropped on an island with nothing" doesn't
really work for "having solar panels to power stuff".

What sorts of things do you wish to power?
will you have to hand carry all the stuff that is available?
What resources do you expect to have locally?
In a "survival" situation your big priorities are food, water, shelter.
It sounds like food/shelter might be taken care of, but not
water (or perhaps "clean" water) since you mentioned a the water
collection system.
I think serveral sheets of thick sheet plastic are a good start.
it will catch water, you can make a lined "pond" for water storage,
solar still, condensation collector, etc.
Water filter/purification tablets might be good.
multi-vitamins.... enough to last you your entire trip.
I cannot stress this recommendation firmly enough: a Swiss army champ knife.
I've cut 2x12s with mine. has many tools including a mag glass which
might be helpful for starting a fire in a pinch, though a good lighter
is light and easy to pack.

I lost mine a couple weeks ago and i'm
amazed at how often i "miss" it for doing all my everyday tasks.
need to replace it soon.
some other things to think of:
several sheets of mylar: light and shiny... can be used for a solar
oven to help pasteurize water/cook food/etc.
Several large "turkey" cooking bags (also for the solar oven)
Space blanket or tarp: if the weather can get cold.... also the shiny
surface could be used in the solar oven setup instead of mylar. the
tarp version can be an emergency shelter.
Wood gassification stove (or instructions for makeing them with local
materials). for efficient cooking and creation of charcoal to help
filter/remove organics from water. I believe there are small designs
that can be made from a couple soupcans.
Solar LED garden light: can provide light, recharge batteries (Hampton
bay has some cheap ones at Home Despot (sic) that have 2 removable AA
batteries. I just used them while camping to recharge my flashlight
batteries.)
I picked up a small solar panel from harbor freight that charges
several battery types( built in:AA/9V...others with "clips") and has a
power octopus to provide 3-12V output for running devices, but i can't
find a link on the web page... if i find the box, I'll look for a SKU.
Small trenching tool for digging. (toilet, water collection, etc)
yoghurt or kefir culture. if you can get milk, this will preserve it
and alow you to make cheese/etc. the whey is high in b vitamins as
well.
Sewing kit with sturdy needles, perhaps leather needles, and strong
thread. (artificial sinew is good.)
you might want to ask this on misc.survivalism...