I am looking for a game that does not have combat, or combat is an inherent failure condition to the point of being effectively impossible without ending the game.
Based on a quick glance at my collection:
Arkham Horror/
Call of Cthulhu: Mostly investigatory. Combat isn't non-existent, but it shouldn't be a desirable option.
City of Mist/
Hard City/
A Dirty World: All focus on noir investigation, but fisticuffs are a possibility, so probably falls foul of your criteria. City of Mist has characters imbued with powers so probably the worst offender.
Cortex Prime: Not really a game, so much as a toolkit for making one yourself, so you can customise it to fit.
Kids on Bikes/
Tales from the Loop/
Things from the Flood: They all have you playing as preteens/teens (not to everyone's taste) and draw from the "kids on bikes" subgenre, where combat isn't typically a thing that happens. And when it does, tends to be hitting something with a hard object and legging it. Adventures in TftL and TftF typically revolve around weird events caused by experimental physics.
Monsterhearts: Teen high school drama where characters are secretly supernatural creatures (as allegory for the adolescent experience). Potential for physical conflict would generally be a schoolyard scrap.
Raven: Gothic horror inspired by the works of Edgar Allen Poe. Ghost stories and mysteries. Threats are spectres, curses and the like, so good luck physically fighting that.
Star Trek Adventures: It's Star Trek, so combat should always be a last resort/failure state.
Vampire: The Masquerade: Specifically, V5. Older editions facilitate a "trenchcoats and katanas" or "supers with fangs" approach, but that's deemphasised by V5's mechanics. Often plays as a supernatural mafia, which has the potential for violence (and there are powers for it), but socio-political intrigue and occult investigation are common.
World Wide Wrestling: Pro Wrestling. Staged fights in the ring are obviously a big portion, but actual combat is not generally a thing.
This has really driven home just how many RPGs utilise physical conflict as a driving force.