The dust bin is secured by a spring latch in the handle of the dustbin. Here is a picture with an arrow pointing at the spring:
[image|1425989]
Make sure this spring is properly seated and hasn't become loose or lost. Also check for any other damage.
If lost, here is a handle assembly for the DC65: https://www.amazon.com/Dyson-966060-01-Handle-Cyclone-Dc65/dp/B00Y363LP8. I'm getting conflicting information if this handle assembly is compatible with the DC75, but maybe you could replace the lost spring.