Unit won't turn on if not plugged in

Greetings, I am working on a couple of Physiometrix PSA 4000 monitors. They work fine on A.C. I replaced the 12v battery, but the units will not turn on if not plugged in. However, if I turn the units on, I can disconnect A.C. power and they continue to function. I have no documentation. I left a message w/ Hospira tech support but am still waiting to hear from them. Thanks for any help, Andy