Can you continue the first Kingdom Hearts game after you defeat Ansem?

No you can't. But you can always start again and try to complete the game properly by getting all of the items and getting to as high a level as possible. And at least it didn't freeze in the credits for you -.-' That was a bit of a back-handed pep talk! What he should have said, if he knew that is, was that if you close ALL of the worlds, including Olympus, with the exception of the end of the world, and get all of the dalmation puppies, as well as complete jiminey's journal, you can see the The World that Never Was trailer, which is a sneak peek at the plot at the second game, where Sora ends up going to, at the very end of the next game. This dark city leads to castle oblivion, though in KH2, you can only go to the groud floor and take the elevator up, for the bottom floors/basement is reserved for the intermission game/chain of memories that plays a huge part in the plot of the 2nd game, as well as the plot twists that were missed between the games. That is the secret ending, it's easier to just look it up on the net. Also if you were referring to me I am a girl. Good luck on unlocking the secret ending. Oh And if you haven't played Kingdom hearts 2 yet you so should, it rules!