Oh I see, oops sorry.
Well I still see two problems.
digitalWrite(SSpin, HIGH);
SPI.begin();
First, this is setting SS high before initializing SPI. This won't matter too much in itself, since SPI.begin sets it high anyway. However of greater concern is that the clock polarity is determined when SS goes active, so it may be the wrong way around (as it is active immediately).
Second, since SS is high initially the first attempt to access it, namely:
writeRegister(CONTROL_REG,0x00);
will not cause a SS low-to-high transition (it already is high). The spec says "The address byte is always the first byte entered after CE is driven high.". Well if it isn't driven high, the address byte won't be read.
I would do something like this:
SPI.begin();
digitalWrite(SSpin, LOW);
SPI.setDataMode(SPI_MODE1);
This means that SS is now low, and you then change the data-mode to the correct value. After this, accessing the chip should start with low-to-high and work correctly.