The only way I can run or use my Pip-Boy is when I equip a Power Armor.
I already tried loading another game, killing myself (explosion, bullets and drowning) but nothing helps ..
Already played for 30 hours and the last thing I want is a restart..
Can you uninstall and reinstall the game but keep your saves? I'd try that if you can. Good luck.
Edit to add: I'm sure you've already tried this but restart your system?