I have a labtec lcs-2514 computer surround speaker system
(the one where everything connects to the subwoofer).
Anyone have any experience with disassembly of
this unit without tearing it to pieces?

Judging by pictures of the subwoofer that I found, you might be able
to gain entry by removing the grille cloth and exposing the driver.
From there, it could be possible to unscrew the speaker and tilt it
out of the cabinet or remove it entirely.

While this may not let you get at the board, it may let you see how
the cabinet is assembled. I would not be surprised to see the
components placed inside and the cabinet sealed with glue afterwards.
You might have to break the glue to loosen a panel and get inside.

William