Checking if the password and SSID are correct is the best step that the technician should take to resolve the issue of a user being unable to access the SOHO wireless network after replacing the gateway. The new gateway may have a different password and SSID than the old one, which would prevent the user from connecting to the wireless network. The technician should verify that the user has entered the correct password and SSID for the new gateway. Assessing the network cables for damage, disabling Bluetooth connections, or updating the firmware are not likely to solve the issue, as they are not related to the wireless network authentication.