Laptop batteries are so-called "smart batteries", which have microchips imbedded. The battery communicates with the BIOS and with Windows. Many laptops will not start without a battery or with a dead battery, even with AC power brick. Computer appears to be "stuck" in standby.
You said: "...Voltage at the plug that goes into DC power jack on computer is correct,19.5V..." Does charge indicator light on laptop show that battery is charging? If, yes, let it charge the battery.
To charge the battery pack
1 Connect the AC adapter to the computer.
2 Insert the battery pack.
The computer automatically charges the battery (the battery indicator light flashes in a double blink pattern as the battery charges).
3 When the battery is 85% full, the battery indicator light turns off. For PCGFX120/FX120K, PCG-FX140/FX140K models, this process takes
approximately 1.5 hours. For PCG-FX150/FX150K, PCG-FX170/FX170K, PCG-FX190/FX190K models, this process takes approximately 3.0 hours.
To charge the battery completely, continue charging for an additional hour. See “Displaying Battery Information”
Battery Indicator Description
Light Status
On --------------------The computer is using battery power.
Single blink----------The battery is running out of power.
Double blink---------The battery is charging.
Off---------------------The computer is using AC power.