I don't think any individual tool qualifies as "indispensable". What matters most is that some solution exists to the common problems of life, such as communication, transport, food and shelter. The telephone could be replaced by Skype, your car by communal dirigibles, the supermarket and your fridge by local farmer's markets and your private house by a staked-out area in one enormous aircraft hangar for your community. The world doesn't need to look and behave like it does today for society to keep working.
Mokalus of Borg
PS - The internet could be replaced by carrier pigeons.
PPS - A lot of pigeons.