So I'm UPDATING my Nvidia GeForce GO 6400 driver from the device manager. Then this window called Files Needed comes up, and it says the following:

The file 'nv4_mini.sys' on WINDOWS driver cabinet is needed.
Type the path where the file is located, and then click OK.

Anything I can do to fix this problem?

Point it to the directory where the new driver you've downloaded is located.I didn't download anything. I simply clicked on update driver from the device manager.

I just tried uninstalling and reinstalling via the device manager. The uninstall worked, but I'm STILL having the same problem when reinstalling. Also, I'm just clicking on reinstall from the device manager page. I haven't downloaded anything. At least I don't think I have.You can't update a driver without first downloading a driver update.
Since your graphics card is a GeForce Go I assume this is a laptop.
In that case you need to download any driver updates from the manufacturer of the laptop.
Also keep in mind updating drivers from device manager is an ineffective way to do so...it normally only checks for updated Windows drivers.
It's always best to go straight to the source which would be the manuf. website as Deerpark suggested...