You should have read the error message. I'm pretty sure your system doesn't meet the minimum requirements to run Dolphin and that's why you're getting that error.
You didn't say which GPU you have, so, I assumed you're running on the IGP from your motherboard. Then we look at your processor, a Core 2 Duo, one which uses LGA 775 socket, and in almost all motherboards compatible with that socket we have old IGPs like Intel GMA, which Dolphin doesn't support anymore since 3.0 era. Said that, you're out of luck, Dolphin will not run in your computer.
Also, you can't update pixel shader, to get a higher pixel shader version you have to upgrade your GPU, but even if you get a dedicated GPU that meet the minimum Dolphin requirements, your processor would still be too slow to run most of the games.
If you still want to try Dolphin in that machine, then you can use very old builds, like r7598 (the last version compatible with PS 2.0a) or r4598 (the last working revision for older Intel GMAs, like the 945G), but be adivised that they'll have a lot of bugs already fixed in current development builds and that you won't get any support in the forums, we only support builds newer than the latest stable release (currently at 4.0.2)...
You didn't say which GPU you have, so, I assumed you're running on the IGP from your motherboard. Then we look at your processor, a Core 2 Duo, one which uses LGA 775 socket, and in almost all motherboards compatible with that socket we have old IGPs like Intel GMA, which Dolphin doesn't support anymore since 3.0 era. Said that, you're out of luck, Dolphin will not run in your computer.
Also, you can't update pixel shader, to get a higher pixel shader version you have to upgrade your GPU, but even if you get a dedicated GPU that meet the minimum Dolphin requirements, your processor would still be too slow to run most of the games.
If you still want to try Dolphin in that machine, then you can use very old builds, like r7598 (the last version compatible with PS 2.0a) or r4598 (the last working revision for older Intel GMAs, like the 945G), but be adivised that they'll have a lot of bugs already fixed in current development builds and that you won't get any support in the forums, we only support builds newer than the latest stable release (currently at 4.0.2)...
Avell A70 MOB: Core i7-11800H, GeForce RTX 3060, 16 GB DDR4-3200, Windows 11 (Insider Preview)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)
ASRock Z97M OC Formula: Pentium G3258, GeForce GT 440, 16 GB DDR3-1600, Windows 10 (22H2)