I started playing Altered Destiny lately, a game I've been after for more than a decade, but when I try to leave the first island by stepping on that giant gray jellyfish thing, the picture of my guy disappears and the game just stops. And I made sure I wasn't carrying the axe. Is there anything I can/should do to fix this?

Dunno, it worked for me. Afaik you got on the floater and it took you to another (small) island.