ECM sensitivity to voltage?

[terror_storm]

So I recently picked up a '91 hatchback with a red top SR swap. Thus far I have not heard it run. It will crank, slowly (the battery is weak), but not fire. The plugs are dry (checked injectors with a noid light, too: no dice) and my timing light does not show any lightning. However, if I turn the CAS by hand with the ignition on, the injectors fire, the fuel pump runs, and my timing light illuminates. My hypothesis is that the ECM will not function during cranking due to low voltage. I've worked on my share of crappy cars with weak batteries and have never experienced this.

Has anyone else experienced this with just Nissans?

http://i31.photobucket.com/albums/c361/jboner1122/2012-06-09_10-17-33_31.jpg

[terror_storm]

Dropped a new battery in and it fired right up.