What you didn't mention though was if you've tried any of the DriverPacks.
Because your HWID is supported through the current release DriverPack Graphics A\D\G\N1\NV4_GO.INF

Now if you've tried DriverPacks and they don't work, then that's something to go on, but I'll need to see your setupapi.log from the failed system.

It is an nVidia NVS 3100M installed in a Dell E6410.

Device Instance ID
PCI\VEN_10DE&DEV_0A6C&SUBSYS_040A1028&REV_A2\4&2A7D5098&0&0008

Hardware ID's
PCI\VEN_10DE&DEV_0A6C&SUBSYS_040A1028&REV_A2
PCI\VEN_10DE&DEV_0A6C&SUBSYS_040A1028
PCI\VEN_10DE&DEV_0A6C&CC_030000
PCI\VEN_10DE&DEV_0A6C&CC_0300

Complication: The driver download from Dell for this card doesn't work with it just installed via Device Manager. There's an INF but you get an error when you try to use it - you have to use the EXE to install it. You can download it below.
Driver link
I get some error about not being able to copy NvCplSetupInt.exe. Unpacking the EXE's with 7zip does not work. Tried some limited editing of the INF file to fix the problem but couldn't figure it out.

There IS a driver that will work. However, it's in a 222MB deployment pack of drivers from Dell. You can get it in the link below
Driver link
It's in the subfolder E6410-xp-A02-R269405.CAB\E6410\xp\x86\video\R260613\Display\
I decided not to extract it and upload since I assumed you'd want to get it straight from them to assure a good "chain of custody".

Keep up the good work guys. This is such an amazing resource. Thanks!