The CPU is worth a look also. If the IRQ pin isn't connected you can have trouble.
You could just check continuity between the CPU IRQ pin and Pokey and PIA.
PIA is a 6520, though could be labelled as 6820 - "Atari part # CO14795 or CO12298 - sometimes no Atari number, Hitachi HD68B21, GTEu G65SC21P" (from AtariMax Jindroush site mirror)