W5100 Ethernet shield and TLC5940

Which Chip are you using?

change line 61 from

#define DATA_TRANSFER_MODE    TLC_SPI

to

#define DATA_TRANSFER_MODE    TLC_BITBANG

Then look at lines 73-79

Change them from

/** SIN (TLC pin 26) */
#define SIN_PIN        DEFAULT_BB_SIN_PIN
#define SIN_PORT       DEFAULT_BB_SIN_PORT
#define SIN_DDR        DEFAULT_BB_SIN_DDR
/** SCLK (TLC pin 25) */
#define SCLK_PIN       DEFAULT_BB_SCLK_PIN
#define SCLK_PORT      DEFAULT_BB_SCLK_PORT
#define SCLK_DDR       DEFAULT_BB_SCLK_DDR

to

/** SIN (TLC pin 26) */
#define SIN_PIN        PD5
#define SIN_PORT       PORTD
#define SIN_DDR        DDRD
/** SCLK (TLC pin 25) */
#define SCLK_PIN       PD6
#define SCLK_PORT      PORTD
#define SCLK_DDR       DDRD

That will use pins 4 and 5 on the arduino I am assuming you are using an UNO (ATMega168)