Leeana, this is considered to be a casual game so I moved your post over to the Casual Games forum. Big Fish sells the game
here. You will be able to download the demo from this page.
The reason the game did not pick up where you left off is due to the following (I googled):
"Virtual Villagers is designed as a real-time simulation, meaning life on your island continues even when the game is closed, your computer is turned off, or you step away. Because time passes continuously, your villagers can age, get sick, or starve while you aren't playing."
You can, however, make an adjustment in the game's speed settings (find this by clicking Menu or Options) by changing it to pause before exiting the game - that way, when you do exit the game, the villagers will not do anything until you return to the game again.
I remember this game well. It came out in 2006. It was so successful that there ended up being sequels and a lot of imitators, and it sort of created its own genre within the casual-game realm. There are puzzles, and it is also a simulation/adventure game of sorts.
There are tips and tricks out there too, for anyone needing a walkthrough or help with a puzzle.