There is no "part number" -- the chip is part of the mainboard.  That's what you need to replace.

It's this one:

http://www.parts-people.com/index.php?action=item&id=5164

The Intel video version is more reliable and will also work.

http://www.parts-people.com/index.php?action=item&id=3509

Thanks, but on the nvidia GPU legislation site, you are required to enter the "Part Number" for the GPU before you can proceed.  I have the 7400 in my M1210 but none of the part numbers I have tried will work.  The HN110 motherboard part number that you linked above doesn't work either.

Has anyone else with a 1210 gone through the settlement site successfully?

http://www.nvidiasettlement.com/

I have an M1530 with the 8400 NVIDIA chip, bought in exactly the right timeframe and experiencing symptoms...and yet, none of the numbers I put in for the part number are working. 

I wouldn't waste much time on it - the fund amount is $2 million - divide that by the number of these chips out there and you'll be lucky to get a coupon for $5.

I own a dell M1210, here is the part number: XG597  it should be listed as:

Module,Assembly,Base Discrete,XPS-M1210