No, you cannot currently get location without using GPS or internet.
Location techniques based on WiFi, Cellular, or Bluetooth work with the help of a large database that is constantly being updated. A device scans for transmitter IDs and then sends these in a query through the internet to a service such as Google, Apple, or Skyhook. That service responds with a location based on previous wireless surveys from known locations. Without internet access, you have to have a local copy of such a database and keep this up to date. For global usage, this is very impractical.
Theoretically, a mobile provider could provide local data service only but no access to the internet, and then answer location queries from mobile devices. Mobile providers don’t do this; no one wants to pay for this kind of restricted data access. If you have data service through your mobile provider, then you have internet access.
In short, using LocationManager.NETWORK_PROVIDER or android.hardware.location.network to get location requires use of the internet.
Using the last known position requires you to have had GPS or internet access very recently. If you just had internet, presumably you can adjust your position or settings to get internet again. If your device has not had GPS or internet access, the last known position feature will not help you.
Without GPS or internet, you could:
Take pictures of the night sky and use the current time to estimate your location based on a star chart. This would probably require additional equipment to ensure that the angles for your pictures are correctly measured.
Use an accelerometer to track location starting from a known position. The accumulation of error in this kind of approach makes it impractical for most situations.