Had issues with my 1-week-old Samsung Galaxy S 16GB GT-I9000 (through Optus in Australia, not rooted) connecting to my home Wifi too.
Everything else seems to work OK, including Kies prog. interface with PC, Android 2.2 Froyo update, GPS etc.
Found the following suggestions when trying to address Wifi issues, apart from ensuring that Wifi is actually turned on, testing that other devices pickup your Wifi OK, testing your unit on a range of different wireless networks etc:
1) Reset SGS to Factory Default settings, power it down and reboot.
2) Power down & reboot Wireless Router.
3) Change Wireless Router broadcast channel to some other values between 1 & 11.
4) Attempt to tweak the "AllShare" app settings if you have it.
5) Try WiFi Fixer app.
6) Tweak the unit's Wifi settings such as Static IP, Sleep Policy and SSID visibility.
7) Examine the Wireless Router's Mac Filtering settings if applicable & tweak/activate/deactivate it.
8) Clear both levels of memory in the unit's ram manager then turning Wifi off & on.
9) Refraining from updating from Android 2.1 to 2.2 (though surely this would be a step backwards in general and dumb that it may help).
10) Change your Wireless Router's Wireless Mode to 802.11g instead of 802.11n or whatever else it may be set to - This is what worked for me using a Billion BiPac 5200N Wireless-N ADSL Router - As soon as I changed it to 802.11g both my SGS and wife's (also 1-week-old) Samsung Galaxy 580 (which also wouldn't connect to our (802.11n) Wifi at all) connected to the Wifi perfectly.
I prefer to run 802.11n on my wireless and am disappointed that these Galaxy smartphones claim to be 802.11b/g/n compatible yet apparently are not, forcing me to adjust my system to 802.11g.