I had no problems for over a year, and then after upgrading to 4.3.2 boom I was having the same problems of being unable to connect to wifi on the iphone at home (other devices worked fine). I upgraded to 4.3.3 but it continued & then I thought I would try online for help!
My iphone was showing it was connected in the settings page, but not in the top left of the home screen, and if I tried to update apps etc it could tell me to connect to wifi.
I tried all of the solutions suggested by others here, except updating firmware because I had no idea how to do that!
I have at last (fingers crossed it continues) managed to solve the problem using a combination of the suggestions here. I will list what I did in the order I did it, just incase it helps anyone else. (Apologies in advance Im no computer expert!!)
1. Settings > WiFi > clicked on my network > Forget this network
2. Settings > WiFi > Ask to join networks > OFF
3. Settings > WiFi> OFF
4. Unplugged my router for over 30 minutes I had tried spells of ten minutes etc before with no luck
5. Switched router back on waited 5 minutes
6. Settings > WiFi > ON
7. Settings > WiFi > clicked on my network > enter router password
As I say I tried other things that worked for others and it didn't help me, but this worked for me & it may help someone else.