It is possible to update the FW with out Internet and if you have a wired connection to the router and can access the web page. Let do some trouble shooting first before updating as doing any FW updates might not resolve the problem. We can definately update if we can narrow down the problem. Can you check the Status/Device Info/Wan section and let us know if you see IP addressing there for WAN, Gateway and DNS?
What ISP Service do you have? Cable or DSL?
What ISP Modem do you have? Stand Alone or built in router?
What ISP Modem make and model do you have?
If this modem has a built in router, it's best to bridge the modem. Having 2 routers on the same line can cause connection problems.
Some things to try:
Ensure DNS IP addresses are being filled in under Setup/Internet/Manual? You can find these under Status/Device Info/Wan section.
Turn off ALL QoS (DIR only) GameFuel (DGL only and if ON.) options. Advanced/QoS or Gamefuel.
Turn off Advanced DNS Services if you have this option under Setup/Internet/Manual.
Turn on DNS Relay under Setup/Networking.
Setup DHCP reserved IP addresses for all devices on the router. Setup/Networking
Ensure devices are set to auto obtain an IP address.
Set Firewall settings to Endpoint Independent for TCP and UDP.
Maybe someone can review your router settings with you using teamviewer.