It sounds like your Touch is connected to your WiFi access point.
To confirm this, go to Safari on your Touch and enter the following into the address field:
http://64.233.187.99/
If you get to the Google Home page, then you are connected to the internet. The problem is with your DNS settings.
Go to the settings page on your touch and select Wi-Fi. On the list of networks your wireless router's SSID should be there with a tick beside it. (If it is not ticked, select it) On the other side of the same line there is an arrow inside a circle. Press this to expand more info.
On the top section headed up "+IP Address+" you will most probably have DHCP selected.
If this is the case you will not be able to enter anything into the +IP Address, Subnet Mask+ and
Router fields. They should have values supplied by your router (if you have the DHCP Server set on in your router). This is ok.
Look at the next field
DNS. This may be blank, but should have a value supplied by the router. It may be the same value as in the
Router field or it maybe the value you typed into the
DNS or +Primary DNS+ field that you typed into your router when you set it up.
The
DNS field should contain the IP address of your ISP's Primary Domain Name Server (Hence DNS). You should have this info in the information you got from your ISP, but if not you can get it from their helpdesk. Your ISP's DNS is best to use when at home as theoretically closest and will hopefully give you better browsing performance.
If you don't have the above info to hand, you can use either of these OpenDNS addresses:
208.67.222.222 or 208.67.220.220.
You should make a note of these in the notes app on your touch. Because when you are out and about you will need them. I would use these in any network except your home one.
Anyway, select one of these addresses and type it into the
DNS field on your touch and then press the return key.
Press the Wi-Fi Networks button right up the top of the screen which will return you to the previous screen and then turn off the Wi-Fi. Press the Wi-Fi switch again to turn it back on.
Wait for the Touch to connect to the router (when the tick appears) and then wait for the padlock to come up if you use encryption.
Once this has occurred, switch back to Safari and type in
http://www.google.com/
Hopefully if all goes well you should not get the Google home page and not the dreaded "+Safari cannot open the page because it is not connected to the Internet.+" message.
Post back with how you got on.