I have a 7200-s with 3X16 DLI, 1 uni card with 2X4 TRM and 1X 4SL2U, 45 DS21 and 1X64 button DSS. I would like to connect battery back up using the Samsung provided cable and 4x 12v batteries. Would anyone know estimated power back-up time? I have sent Tech support an email days ago but no response!!!

One factor that is going to matter is the capacity of the batteries you plan to use.

I was planning to use 4x12v car batteries according the instructions from samsung NICAD or lead acid rating not less than 6AH and no more than 40 AH.

Don't use NICAD, use the Lead Acid.

The bigger the battery the longer it will hold up.

The actual time will depend on how much the phones are used during the blackout, what condition the batteries are in, etc

Ask tech support for the maximum draw of the system (or work it out based on the voltage and amperage that the Power supply is rated for (this is written on the power supply)).

I have it but as our power is 240v vs your 120v it may be different.
Then work out how long your batteries will last under that load and you have the minimum.

I think what you should be looking at like nameless said are lead acid the type you would see inside an alarm panel.The manual does have some power stats in it It appears the system may draw up to 48V 3A .I'm sure that is a maximum and they do list by device what it draws in the manual.But like mentioned ,useage will also matter.A user on an analog trunk will draw more with powering the relay on the trunk card.

Use deep-cycle lead acid marine batteries. The connection posts work well in these types of installations and the batteries themselves hold up well when not being tasked- they hold charge almost forever.

Look at OMI Communications. A lot easier.