The sun roof control switch has one position for closing and two for opening. The opening is;
Tilt where the back of the sun roof lifts up, but it does not start moving back
and
Open, where the roof is now tillted and will start moving back. This requires the switch to be pushed one step further.
On the passenger side of the sun roof rails there is a Micro Swith that determines whether the sun roof is open or closed. If the sun roof is closed the motor will will cause the sun roof to open and tilt when the first step is pushed on the control switch. As soon as the sun roof opens the motor will stop running untill the second step is pushed (translated, pushing harder on the switch)
If for some reason this micro switch is defective or out of adustment than the motor will not run trying to open the sun roof. However if you push the control switch that much harder to reach the second step, the motor will run anyway because the micro switch is by passed by pushing the control switch.
However you state you think you can feel the relay working, with out an electrical measurement this may or may not be important.
It sort of sounds like the open relay is defective, from the picture you have there is two of them on that circuit board. To replace them it looks like they have to be soldered in place. Standard circuit board repair methods. Just not usually seen in a car. Saturn parts indicate that relay is available. That last URL seems to indicate something is available.
Actually the Sun Roof is one of the reasons I like my Saturn, but then again it is a driver not a trailer queen. I hope this helps some for you, I spent a ton of money fixing mine. You are ahead of me, you got it apart hopefully with out breaking everything around it.

 

So an interesting thing happened after I posted up the pictures. I decided to look a little closer at the module to see if there was anything visually noticeable. Of course, I found a black ring around one of the solder points which is an indication of breaking / broken solder which could mean it’s not getting a good enough contact. Anyhow I decided to try reinstalling it in the car after all of this just to see if futzing with it jarred it around enough to make a contact. After I had it all reinstalled (switch and module still just hanging) I fired it up and it started working. However it randomly stops working so I give the module a little smack and it starts working again. Tomorrow I am going to get it re-soldered and I will post up in a few days to let you all know if that solves the problem.

 

K, I just had it re-soldered. Sat there for a few minutes just opening it and closing it. Did not stop working once. So far so good.