trackpad light goes out

New iMac. Trackpad in use on old iMac. Batteries low about the same time. Set it aside for a couple of days, set up new iMac, migrated everything from old iMac. Want to start using trackpad with new iMac. Put in new batteries, correctly with "negative" end towards door. Push "on" button, little light comes on, then goes out, then blinks once, then goes out again. All this with Trackpad Preferences pane open and "searching." Trackpad never found by new iMac. Guy at Apple Store told me the Trackpad has not been changed and my old one should work fine with the new computer. So, what's wrong?