Hi,
I recently picked up an A2000 that had been sitting for several years. It showed similar symptoms to yours when I first powered it up. If you haven't already, try removing and reseating the 68000. While the CPU is out, check the socket for battery corrosion.
In my case, the corrosion had spread to about half the pins on the CPU socket, and most of the legs on the CPU were oxidized all the way to the plastic case. I ended up following the steps in this thread (
http://www.amiga.org/forums/showthread.php?t=40875) to replace the socket. I cleaned the oxidation from the legs on the CPU, reinstalled it, and the system booted to the insert floppy screen.
As part of the work, I checked the continuity for each pin on the CPU socket, then rechecked from each CPU pin once I reinstalled the cleaned processor. Most of the pins are available on the CPU slot or a nearby via. Pages 2 and 13 in the A2000 schematic (
http://amiga.serveftp.net/schematics.html) were very helpful here.
Robert