blaupunkt head unit

the  Sacramento should have loads of get up and go... i would suspect a pinch or short on a speaker wire or as DYohn suggested you are going through a factory amp possibly... the Camry does have an amp under the passenger seat... did you use the amp integration harness or did you use the deck to speakers harness and bypass the amp?

if you look slightly to the right of the radio you'll see that the wiring from the amp comes back up to the radio and couples to a shorting connector... this way the vehicle is wired for both an amp or for the non-amplified radio only option... i usually unplug this set of plugs and plug directly into the connector with a Metra 70-1761.... is this the plug you used or did you use the 70-8112? ( doubtful since the Sacramento doesnt have dual pre-outs)

Sounds like there is a crossed or shorted out wire or you have a bad head unit.  I don't know much about the blau line of car radios but make sure your unit is grounded real good and the antenna is connected.  Some units use the antenna as a ground. 

Another thing you can try is to disconnect the entire unit and rewire the harnest wire by wire as you test it.  Wire the 12+, acc, ground, amp on if needed.  Than wire up one speaker and test the unit.  If it plays louder just go speaker by speaker.