Well, it turns out the issue is more intermittent than I thought.
After replacing the hard drive to try a Windows 7 install (without destroying the install it came with) it required the dance with the external monitor to get it to boot again. Went into the BIOS and toggled external/internal monitor, and it worked again, allowing shut down, sleep, hibernate, without any problems.
I then remembered I had an SSD to pop in there, and did so. Same issue, but have not been able to get it to start up at all, through any combination of battery, power, monitor, or anything similar plugged in.
When I get home tonight, Im going to check the voltage of the BIOS battery. I'm not familiar with the architecture of these machines -- is the BIOS battery strictly for keeping the RTC running, or does it also preserve BIOS settings? Older machines tend to require the battery to preserve the settings where newer machines will write them to NVRAM.