I updated my GPU driver to 17.7.2 (latest according to Radeon Settings) and now the the core clock stays at 300MHz, memory clock at 150MHz and the GPU activity jumps from 0% to 100% all the time (both during intensive tasks like games and when idling). (Also worth noting: I can't adjust the core and mem clock in the built in overclocking tool:)
I used DDU to get rid of all old AMD drivers and reinstalled 17.7.2 again, because I though something went wrong while installing it, but to no effect.
Update: I tried installing older drivers but when installing the software it gave me the error 182 (hardware cannot be identified) message. (Tested with 17.4.4 and 17.7.1)
CPU: i7 4770 @3.4Ghz
GPU: Sapphire Nitro R9 380X 4GB
RAM: 16GB 1600MHz
MOBO: AsRock Z87 Pro4
PSU: Sharkoon WPM 700W 80+ bronze (never had any issues)
OS: Windows 10 64bit
Screen: BenQ XL2411 (1920x1080 144Hz, DVI)
Message was edited by: Matt B We have updated the title of this discussion with relevant details to better describe your issue.