Given the symptoms, it's very likely that there is at least one open circuit line in the register address bus (RGA), or possibly the DRAM data bus (DRD). Refer to the schematic for details:
http://amiga.serveftp.net/Schematics/A2000_schematics/A2000_R6_schematic.pdfBoth of these buses are common to U200 (Paula) and U201 (Denise); use a scope to check for activity on all 8 address lines at either U200/201 and 16 data lines, and it should quickly be obvious what's not working. From there you'll be able to work backwards to pinpoint the open circuit track/via.
The register address bus is created by U101 (Agnus), so an open circuit line can be also caused by one or more bad contacts in the PLCC84 socket.