Can anybody identify this component (SPRAGUE 663044-4) on this vintage electronic?
Those are small PCBs with a passive filter network in a single inline pin package potted with epoxy. The schematic on the far left within the dashed lines shows the components of a single board (notice, the pin-out for that part of the circuit is labeled 1-7), and it is not drawn for the others (presumably identical) to save space. You can replace them with what is inside the dashed line on the left side of the schematic, but it is unlikely to be what is broken, since everything inside is a passive (just caps and resistors).