A white remote should work fine.
It could be possible that the white remote was paired to work with only one Apple device. I'm not sure if pairing changes something in the remote, or something in the device or both, but it is supposed to make sure that the remote will only control one device at a time. Not 100% sure this is your issue, but worth a try. Otherwise your remote may have a dead battery or I think the new remotes come with a plastic tab you need to pull out from the battery to allow the battery to contact the remote...maybe yours still had this plastic protecting the battery?
I just Googled and found this:
http://support.apple.com/kb/HT1555
To unpair you do this:
To unpair your Apple TV from a remote
You can use any Apple Remote to unpair Apple TV from a remote. Note: If you lose the Apple Remote that you paired with Apple TV, a replacement remote will not work until you unpair Apple TV from the lost remote.
Press and hold the Menu and Previous/Rewind buttons on a white Apple Remote for 6 seconds, or the Menu and Left buttons on an aluminum Apple Remote for 6 seconds.
You can also use these steps:
1.Choose Settings > General > Remotes from the Apple TV main menu.
2.Choose Unpair Apple Remote.
When youve successfully unpaired a remote, Apple TV displays a broken chainlink symbol () above a picture of a remote. You can now pair Apple TV with a different remote.
Or to change the battery:
http://www.instructables.com/id/How-to-open-the-Apple-Remote/