In ST1 Phantom Menace, the first time Darth Maul encounters Qui-Gon Jin in the desert, he is using the same double lignt saber as always, yet he only uses one side against the Jedi. Why?
It would have been FUCKING COOL if he had unleashed the dual lightsaber when he took on Obi-Wan and Qui-Gon at the same time, but whoever put the trailers together spoiled that.
My guess is the kick-ass factor. Don’t shoot your wad right at the start.
Surprise. Remember, Jedi are not used to fighting opponents with lightsabers. The Sith are unknown and Jedi don’t fight each other (except for training purposes). The only reason Darth Maul does as well as he does against both Qui-Gon and Obi-Wan is that they’re not expecting an opponent like him, and certainly not one with a dual lightsaber. So my guess is he was saving it that first time.
Not only for dramatic effect, but in novels, etc. we see Darth Maul is extremely overconfident in his own abilities. He probably figured he would need to take out all the stops to beat one Jedi.
Maybe the batteries were low the first time! 
In the directors cut, we see Maul going back to his hoverbike looking for his car charger.
If you ask me, fighting with a double lightsaber would be awfully risky. Most of the moves seem to be based on staff fighting, but when you hold one end of a staff under your armpit, it doesn’t cut your arm off. So when it’s one-on-one, it’s best to just use one blade and keep it pointing away from you. On the other hand, when you’re double-teamed, you need to have both blades available to block both of your opponents’ blades, so you have to accept that extra risk.
I don’t know about the surprise factor–he was legitimately trying to kill Qui-Gon the first time, it seems, and I’m not sure if he knew that the witnesses on the ship would care about it. More likely, he had never fought a Jedi before and was trying to get a good understanding of his abilities.
(Things derived from EU material follow) Maul was raised with a pathological hatred of the Jedi, and Qui-Gon was reputed to be the best swordsman of the order. Thus, Maul would reason that if he could learn to beat Qui-Gon with one lightsaber tied behind his back, he could easily take out any other Jedi with his full resources.
that Jedi and Sith were derived from the same source and both still adhere to a code that is beyond good or evil. I thought that if he had used both, it would have been an unfair advantage and a violation of that code.
I’ve never heard of such a code. Jedi avoid killing when possible, Siths don’t. Qui-Gon and Obi-Wan didn’t shy away from attacking Darth Maul although they were two against one, which seems more of an unfair advantage than having two blades.
Maul’s Code is to tattoo your face, don’t say much, go crazy from ink poisoning, and get chopped in half by just standing their like and idiot. Similar to the Boba Fett code of wear armor, don’t say much, go crazy from suit rash, and get killed by a blind guy and a big hole with a stomach.
In any event, Darth Maul as kicking Qui-Gon’s buttocks across the Galaxy with just one blade.
Star Wars Tales featured a short story which told how Maul first came to use the double-blade. Sidious ordered him to kill a Jedi hermit who was skilled enough that he was able to pin Maul with a simple stick. Embarassed, Maul secreted away and fused two sabers together. When he attacked the hermit Jedi again, Maul allowed himself to be pinned again, but in such away that the other end of his stick was behid the Jedi. And zap: dead Jedi.
“A trick” he cried.
“No” said Maul. “Simple victory.”