Opinions may differ, but I would put the threshold of replace vs. repair at around 70%. It's far easier to repair a few posts and bad boards than tear down and rebuild. For me this would be easy, but would also depend on the design and whether I am happy with it, and how well it is done to begin with. Since the joists were only toe-nailed, I'd also inspect the ledger board connection to make sure that a) it's not rotten in places or letting the house framing rot, and b) that it has sufficient fasteners to hold it to the house framing. Google "deck failure" if you want to see what bad design/construction of decks looks like.
To replace bad posts, jack up the beam near the bad post and cut/pull nails as needed to free the old post, and install the new one in it's place. If the post doesn't have to look good, use incised treated wood with galvanized brackets and nails, paint any cuts with wood preservative. If the post is appearance grade, either use clear cedar or "sunwood" or un-incised treated wood and let it season before painting.
To install brackets, sink the toe nails so they are at least flush with the surface of the joists, then wrap a hanger (use Z-max or similar if they're treated) and install using the correct nails or screws. By "correct" I mean galvanized 9g joist hanger nails or Simpson hanger screws, and 16d nails where called for for LUS hangers for instance. The LUS hangers use longer nails for extra security.
Resist any temptation to sister or splice in sections or bad posts, joints, or boards. Use good quality coated screws in place of nails for the deck boards unless you're trying to match existing nails.