I don't know how to recover your partition. Should be able from
terminal to get it similar to:

"chown -R 777 /path/to/partion"

I don't have the exact syntax... I always have to look up the
permission stuff since I deal with it pretty rarely. Googling "change
partition permissions" should give you further information. You
should be able to permanently set this up during auto mount, also. I
would remind myself or figure out how to do it by googling
"automatically mount partition with read write execute permissions" or
similar.