This sounds like a heat-soak issue rather than a pure BIOS misconfiguration. On systems like the U59, thermal protection can prevent POST if components haven’t cooled below a threshold, which explains why a 10–15 minute cooldown works. Unfortunately, most OEM BIOS setups don’t allow fully disabling thermal management at boot. You might want to check for a BIOS update, clean or replace thermal paste, and verify fan headers are detected properly at startup.
Side note — I see a lot of similar “no reboot” problems in my day job as a Los Angeles personal injury lawyer, where hardware failures end up tied to downtime claims, so documenting this behavior now could be useful if it’s under warranty.