Weird. The "base" package is actually the most important package and
should be included in the haskell-platform.
Anyway; you could try to do "cabal install base" or so.
cabal-install cannot install base; it is and must be part of the compiler.
The error does not say that base is missing, it says that base is present but broken (stat() is a libc function, not part of base).
The recommendation to check with #gentoo-haskell, however, is a good idea; it's clearly a problem with the Gentoo package.