There's nothing inherent to science to say it couldn't shed light on what you think is exclusive to subjective conscious experience, one way or another. The point of science is to try and understand, whichever way that leads - as doldrugs pointed out, it shares this with mystical/practical religion. Given the particular record of science in recent history as mostly super-reductionist and often inhuman and unethical, it's no wonder that it seems antagonistic to people with holistic or mystical views - but science is not one paradigm, but is the wider body of knowledge that evolves over time (eg complexity and systems thinking seem to be slowly superseeding reductionism in some areas of science)
Imagine if 'science' discovered that in some quantum way, all matter since the big bang is entangled and connected, and that this is analogous to the idea of brahman, the ground of being and somehow provides a mechanism for what you (and i) have experienced of consciousness and its seeming separation from the physical body and connection to the infinite? If science ended up with theories like that would you be more recpetive to it? if so that would seem like cherry picking

- the point in science is you can have favourite hypotheses that you want to be right, but you have to accept the results and fit your understanding around them (or do better experiments) - or as buddha might say 'don't become attached to a worldview, or to certainty'.
...
I've struggled through Godel several times in other people's books (eg loads in roger penrose, and in douglas hoffstaeder) and understand it while i'm reading it (honest

) - he was mostly working in response to some effort on the part of the mathematicians of the day (forget the name [hilbert]) to finally make a complete theory/system of maths that includes all the disparate bits together - Godel came up with a method to disprove that it would be possible to ever fully define an arithmetical system EDIT: from wiki:
Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory.
and
For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.
(it gets much worse than that).
It's also connected to the liar paradox 'this sentence is false', and an example of recursion. The theorem says nothing that denies the power of human understanding (which is probably based on strange loops itself anyway) - after all, godel understood the incompleteness theorem.