A 24-hour car rental is not available on Chang Island, but in Bangkok itself. There are two main roads leading from Bangkok to the piers to the island, each just over 300km. Take Highway 3, then turn off onto Highway 344, get to Ban Bung, turn off again onto Highway 3. One of the signs will be for the crossings at Changu.
There is also a road that continues Rama IX, Srinikarin road. It connects to Highway 344 and you can follow it to Trat to the ferries as above. The price for renting a car from Bangkok to Chang starts from 3000 THB per day. If you book online, and in advance, car rental to Chang Island can be found quite inexpensively, up to 4000 THB.