If you were unsuccessfully trying to play Resident Evil 7 while below or around the minimum system requirements, you might want to patch the game and see how you fare. The reason I'm saying this is because a recent update has added support for older generation CPUs, or more specifically, the game no longer requires the SSSE3 SIMD instruction set.
What this means in practical terms is that Resident Evil 7 is now capable of running on CPUs that are well over a decade old! You mileage will obviously vary as the developers aren't really capable of performing miracles, but if you're around the minimum system requirements you might just get to play it.
That said, I would still strongly urge you to upgrade your PC. You don't have to immediately make the jump to the latest and greatest as that is a rather expensive prospect, but you can easily find mid-ranged cards and CPUs on fairly deep discounts these days. I would recommend aiming for the outdated "powerhouse" hardware as you'll usually get decent performance at a reasonable price. Just make sure to shop around, and good luck!