Since the sensor board doesn't seem to have pull-up resistors for the I2C-bus, can you try 4k7 pull-up resistors from SDA and SCL to 3.3V ?
That would perhaps remove the false hit for 0x77.
Thanks for the photo, but the photo at deal-extreme is better.
The compass seems to be something like "MEMS G2120M", but I can't find a component like that.
The baromic sensor (with ADC and perhaps the EEPROM inside) doesn't even have a number on it.
This is the page for the HDPM01 at the manufacturer site: http://www.hoperf.com/sensor/app/HDPM01.htm
The "datasheet" and the "compass module programming guide" together provide enough information to write your own code.
It seems that ready-to-use example code for the Arduino is not yet available.
I found this : http://jeelabs.com/products/heading-board and with a link to code. But that code seems to be for the compass.
Someone wrote this code : CCS :: View topic - Help to interface with HDPM01 compass module!
What about tossing this sensor away, and buying a decent sensor board ?