OK, I wouldn't use pins 0 and 1 with a touchscreen as that's used for programming. Here's the hardware serial port pinouts:
Name RX SAM3X Pin TX SAM3X Pin Description
Serial RX0 URXD 0 TX0 UTXD 1 Connected to ATmega16U2, serial programming, serial monitor
Serial1 RX1 RXD0 19 TX1 TXD0 18 USART0, Touchscreen A?
Serial2 RX2 RXD1 17 TX2 TXD1 16 USART1, Touchscreen B?
------- --- RXD2 52 --- TXD2 65 USART2, UNSUPPORTED
Serial3 RX3 RXD3 15 TX3 TXD3 14 USART3, ?
SerialUSB --- ---- -- --- ---- -- Native USB Port
Its a bit convoluted ... please re-check your connections?