It SHOULD work WITHOUT the AC adaptor.
Its designed to be used with a 9V battery, ~OR~ the OPTIONAL AC adaptor.
If you have a cable plugged into the INPUT of the pedal, and it has a fresh battery in it, it should work. It WON'T work if there is no cable in the input jack.
So make sure you have a fresh battery. If you tap the 2 terminals (on the battery itself) to your tongue's tip, you can tell how much juice it has left (dont worry it wont hurt).If its kinda weak, just a slight tingle, its low and probably doent have enough juice to run the pedal. A fresh battery will give you a very solid sensation. Try to find the freshest battery you can find, or go buy a pack. Id buy a big pack of 10, just so you wont have to go get more in a month or so.
Also, DONT leave a cable in the input jack, or you will drain the battery OVERNIGHT. (which is why the ac adaptor is popular, because the battery method requires more maintenence, you can leave a cable in the jack with the AC adaptor because there is no drain on the battery. The AC adaptor will power the pedal WITH or WITHOUT a battery in the battery compartment, it doesnt matter. Whenever you put in the AC adaptor, the battery is bypassed and not used (I dont think) BTW- the Boss AC adaptor is sold seperately, never comes with any Boss pedals, but is availible for $20 at the store, ~or~ if you have multiple pedals put "Godlyke Power All" into Google, its a great $40 system that lets you power multiple pedals on the same AC adaptor through a daisy chain.)
I actually run all my pedals (Classic Crybaby, Maxon OD-808, Visual Sound H20) with the standard Boss AC adaptor going into a Godlyke powerall daisy chain. You dont have to use the godlyke powerall with the godlyke cables, they work just fine with the standard Boss AC adaptor.
Tone purists prefer Batteries because they tend to be less noisy and sound warmer. The difference is very small, but the AC adaptors prove to be very useful for their simplicity especially in live situations.
Have fun, Im not a Boss fan, but I like those choruses..