Both RAM sticks work individually but the PC fails to POST when installed together

For two modules, A2 and B2 are normally the correct slots, so the fact that A1 and B1 behave the same makes a simple slot-selection mistake unlikely. With one stick installed, enter the BIOS, load optimized defaults, save, shut down completely, and then install the second stick. Make sure XMP is still disabled during the first boot. If it still fails, try manually setting a conservative memory speed rather than enabling the advertised XMP profile; two modules can fail memory training at settings that each module handles individually.

Run MemTest86 or MemTest86+ with XMP disabled and the BIOS at default settings. Test each stick separately in the slots you know work, then test the pair together. The goal is to determine whether one module produces errors only under load, or whether the problem appears specifically when the memory controller has to initialize two modules. Also compare the reported speed, capacity, and timings for both sticks; they may not actually be a matched kit, even if they look similar. A long test is useful, but you should first see whether either stick immediately reports errors.

If both modules pass individually and the pair still cannot train at default settings, the remaining possibilities include an incompatibility between the modules, a problem with the CPU's integrated memory controller, or poor contact in the CPU socket. Check that the sticks have matching specifications and are from the same kit if possible. If this started after removing the CPU or changing the cooler, inspect the LGA socket for bent pins and make sure the cooler is not overtightened. A BIOS update may also help with memory compatibility, provided the system remains stable enough to perform it safely.