yes that's the remote half of the key.
Honestly for that price i would just go on ebay and try your luck on getting the flip key from a4 of the same generation but later years. You have to program it anyway so might as well try that route.

 

Also, my cruise control doesn't work. We read the Manuel, and it said that it runs off of the same fuse as the taillights. But the taillights work. Any thoughts?

 

I did a little research, and I think I found the problem, something with the vacuum servo...?1996-2001 Audi A4: Reliability - Consumer Guide Automotive

But it says that it should only happen to the '96's, oh well, that's probably it.