首先,表达含义不一样啊~
With something she needed to buy,she went to the marketplace.
这句话是with+不定式的结构,不定式表目的.
译句：（因为）有要买的东西,她去了超市.
With everything she needed bought ,she went to the marketplace.
而这句话是with+done的结构,表示已经完成的动作.
这句话的后半句是你自己写的还是书上原话?按理说不应该是marketplace而是home吧?
译句：该买的都买完了,她回家了.