I bought my BOSU from Target and it was broken AND missing the pump. On mine, the blue rubbery top was mostly detached from the bottom. I couldn't just push it back into the groove. It sounds like you have the same problem. It might be fixable:
The tension of the round base is controlled by two bolts, one on each side of the BOSU. If you tip your BOSU on its edge you can see them on each side of the BOSU on the black plastic base. Basically, there are only two bolts on the BOSU, and either one will work.
Deflate your BOSU. Unscrew one of the bolts from the side of the black plastic ring, and you will notice that the groove where the blue rubbery part is supposed to go widens and loosens. Push the lip of the ball into the groove, then have someone hold the two ends of the black plastic base together while you re-tighten the bolt, and voila! Your BOSU is fixed.
I was a little disappointed that my brand-new, sealed box included a BOSU in need of repairs and no pump. Pretty lame.
As for BOSU-specific workouts...I'd love to hear about those, too! I've been doing Tracey Staehle's Circuit Zone and Core Blast, which both include BOSU, and I've tried some of Cathe's step work on it as well.
