Very cool find!
Is there any video output at all, or just a black screen? Any beeps from the keys (assuming you have it hooked up to some kind of monitor with speakers)?
You might as well try re-seating any socketed chips, yes. It sometimes fixes a bad contact and it's not like it costs anything. Be gentle when disassembling and reassembling the machine, the plastic case can go brittle with age.
You say you have a scope, so a good next step is to try checking the following pins on the 68000 CPU:
Pins 14 and 49: Vcc (should be 5V)
Pin 15: 8MHz clock signal
Pin 17: /HALT (should be high)
Pin 18: /RESET (should be high)
Pins 1-5 and 54-64: data lines (should show activity)
Pins 29-48 and 50-52: address lines (should show activity)
There is a service manual out there. It does assume that you'll have a diagnostic cartridge and a ready supply of custom Atari ICs, but it still has some useful troubleshooting guidelines and an overview of system operation: http://www.atarimania.com/documents/ata ... manual.pdf