I don't own an Apple Thunderbolt Display, but know a thing or two about Firewire (Oh how I miss thee). Firewire 400, IEEE 1934A, has two port variations. 4 pin port found on many DV camera and 6 pin port found on old external hard drives and the original iPod. Firewire 800, IEEE 1934B, is what is on the back of the ATD.
I'm thinking if the Firewire 400 cable you have is too big, it is a 6 pin port and you need the 4 pin variety. You might be able to find a 6 pin to 4 pin adapter, or just buy a Firewire 800 to 400 4pin cable.
I hope this helps!