It should be pretty much plug in and play. You have mentioned you have calibrated it, but have you checked the Button Config? Just going with the easy things first.

If that is all fine, do you have any other applications running that could interfere with anything? If you are running the steam version, you might need to check in the steam controller settings as something might be wrong there (I don't use the Steam version, so I am just guessing here). There is also a third party program called DS4windows that is commonly used to allow a PC to properly see a DS4 controller for programs that don't natively support DS4.

Other than that, I don't really know. Like Vahlnir said, I just plugged in and played.