I think you will find that your ST780 comes with WEP encryption enabled. They normally put the key on a label on the bottom of the router.

Just to prove your wireless connection will work I suggest you access your ST780 with the desktop and disable encryption and set "New Stations are allowed Automatically" for new devices.

Try to access the Internet with your laptop now.
If it works set your encryption to use WPA-PSK , WEP can be easily compromised and there can be problems with the key generation with diff mfr's, and try to connect again.