ADXL345 doesn't work

I am trying to get data from an ADXL345 but it doesn't work. I tried I2C and SPI connections and both failed. Here is how I connect the ADXL345 to an Arduino uno:

I2C:

ADXL345 -> Arduino

VCC -> 5V or 3.3V (ADXL345 has a regulator so it doesn't matter)
GND -> GND
SCL -> SCL
SDA -> SDA
CS -> 5V or 3.3V

SPI:

VCC -> 5V or 3.3V
GND -> GND
SCL -> 13 (SCK)
SDO -> 12 (MISO)
SDA -> 11 (MOSI)
CS -> 10 (SS)

Moreover I used every available adxl345 library I found and all failed to retrieve data. For example:

Adafruit library couldn't even connect with the module.

SparkFun library could connect (I think) but the data was always: x = 0, y = 0, z = 0.

As far as I know my connections (I2C, SPI) are good. So what the problem could be. I just bought this module, could it be broken?

(ADXL345 has a regulator so it doesn't matter)

The ADXL345 chip doesn't include a regulator so I guess in your case the breakout board includes one. So please post a link to your board because p.e. the Sparkfun board doesn't include a regulator.

The ADXL345 cannot work with the 5V I/Os an Arduino UNO provides. So you have to use a level converter. Maybe your board includes one but I don't have that information...

It's this one ADXL345 3-Axis Digital Acceleration of Gravity Tilt Module AVR ARM MCU Arduino | eBay

There do not appear to be level shifters on that board, so it may have been destroyed by connecting to 5V output pins.

It has resistors to reduce the 5V

briler:
It has resistors to reduce the 5V

No, it doesn't. The resistors on the board are pullups. I assume the same as jremington, the chip may have been destroyed already by the to high voltage.

You should only buy boards that are documented with schematics or at least a very detailed connection diagram. The board layout is very simple in this case so the schematics can be guessed from the photo but if you want to correctly set up such a board without a deep background knowledge you should buy a dozen of it to have enough spare if you connect one wire incorrectly.