First off: Is there any battery leakage on the board?
I'd test the voltage coming out of the battery pack, like the person did in this post about Starship Troopers:
https://pinside.com/pinball/forum/topic/sst-not-holding-memory-after-battery-swap
In the attached image, you'll see VBATT and GND1 outlined in green. If the voltage is low, try different new batteries. If that doesn't help, try to determine if the battery pack is attached to the board properly. It's possible a solder joint or two were damaged when the old batteries were removed.
Also, this is from PinWiki regarding batteries and how they supply voltage to the non-volatile memory:
"Adding a connector between the battery pack and the MPU board is a good idea. In doing this, the battery pack can easily be removed from the MPU board. Plus, if the batteries are forgotten, and do leak, the MPU board may not have to be removed to add another battery pack. A 3 x AA battery holder is the typical recommended replacement. If only a 4 x AA battery holder is available, a jumper can be soldered in the first battery position. Likewise, a diode can be placed in this position instead. Using a diode instead of a jumper will prevent the batteries from being charged and 'cooked' by the game if blocking diode D201 on the MPU board fails. Keep in mind that a second (redundant) diode added to the circuit will reduce the backup voltage to the RAM memory by .5 to .7 volts. Install a 1n4001 or 1N4004 diode in the position closest to the last + terminal (where the Red Wire exits). The banded side of the diode must be pointing in the direction of current flow, which is towards the (+) terminal marking on the MPU board, and away from the battery pack.
On the MPU, solder the battery cables: positive (red wire) to the "+" pad and ground (black wire) to the "-" pad.
Since the MPU board is already out, another good practice is to check the D201 blocking diode. An open blocking diode will not allow the battery pack voltage to pass through to the non-volatile memory, and the newly installed battery pack will be ineffective. Conversely, a shorted blocking diode will allow the board's +5vdc logic power bus to pass through to the battery pack. This in turn, will charge the batteries, while the game is turned on. Alkaline batteries do not like being charged. They will heat up, and fail rather quickly. In worse cases, the new batteries can even leak or explode if charged. Testing the D201 diode is quick and easy, and worth the trouble checking it out. When in doubt, replace the D201 diode with a 1N5817 (a 1N4004 will work in a pinch), or add a redundant 1N4004 to the battery pack. Once again, if a second (redundant) diode is added to the circuit, it will reduce the backup voltage to the RAM memory by .5 to .7 volts
Testing the D200 diode is a good idea too. The D200 (1N5817) diode is used to keep the backup batteries from powering the complete MPU board when the power is off. A symptom of a failed D200 diode are batteries which deplete rapidly." - https://www.pinwiki.com/wiki/index.php?title=Sega/Stern_White_Star_Repair#Relocating_the_Battery_from_the_MPU_board
The D200 & D201 diodes are outlined in purple in the attached image.
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