See this thread:
https://gbatemp.net/threads/ps1-reads-backups-but-not-original-games.587436/ especially post #7. It contains the – for me – most plausible explanation: The drive with legit disc and the modchip give the license string at the same time. This results in nonsense and the legit disc is rejected.
It is hard to do anything about this when not knowing what chip (what code) is used and if it is (fully) compatible to the PU-8 and how it gets installed correctly.
A new modchip, MM3 or PsNee, should solve the problem. I've yet to encounter a readable disc (legit or burned) that my PS1 with PsNee doesn't start.
Since backups do start, you could also burn a Tonyhax boot disc and ironically use the "nocash" unlock for starting legit discs.