Hi,
Not sure if this will work for you, but my Auntie has a similar problem with her Galaxy 551 and through searching in the internet I found a way for her to connect successfully to wi-fi again:
The best solution I know as of now is to use the "Allshare" app to connect to the wi-fi. Just click it then press "Ok" if it prompts that it needs internet connection, and it properly connects to the wi-fi (as opposed to turning on the wifi via the drop-down or in the settings menu.
It's good if you already have it. If not, I think you can download it in the market.
The second solution which works but I do not want to use is to use a static IP Address. You can set it on the Wireless Settings. The reason I don't like this solution very much is that I am not sure if it works on all routers, since routers may have different configurations.
I hope you solve your problem soon so you can enjoy your phone!