Since Chip RAM does work (otherwise the machine wouldn't ever boot up w/o Fast RAM) and Copper graphics as well, I'd guess a problem with the chipset (internal) address bus - either on the Agnus or on the Denise side (so Denise' requests get garbled). The PLCC socket may be a very good candidate - possibly just swapping Agnus improved a bad contact, but if the socket isn't looking too well it may not hold for long...
Did Paula sound work? Disk DMA seemed to be working, too - so in theory it could only be the Denise socket, the Denise chip or a trace leading there.
