OK that's great. Exactly the same setup that I have. Driving a single mobile base, regardless of how many handsets you use, should not be a problem at all.
Do you happen to have a working corded phone that you can plug into the back of the OBi200 temporarily just to test inbound and outbound calling? If that phone worked it would at least tell you that there's something going on between the OBi200 and your cordless phone base. Worth a shot.
I'm wondering if there's a defect in your new OBi200 and if you should replace it while it's under warranty.
Try the troubleshooting that I suggested above with a corded phone. If that testing fails, contact the vendor you purchased the OBi200 from or contact OBiHAI directly to see about replacing the unit.