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Thanks for the prompt response! The rate is 115200. I am using the USB port of a Dell Optiplex 755 which is the same hardware I was using previously with the Duemilanove. Here is the source code:

#include <Spi.h>

// Melexis definitions
#define MLX_START_BIT 0x80
#define MLX_RESET_PIN 8
#define MLX_ERRB_PIN 9

#define SER_READ_DELAY 10 // in microseconds

#define GAUGE_LOOKUP { 0x00, 0x10, 0x30, 0x40, 0x60, 0x50 }

#define OP_ZERO_GAUGE 0x0
#define OP_R_U_THERE 0x1
#define OP_SET_GAUGE 0x2
#define OP_DEBUG 0x7

#define ACK_CODE_BIT 0x80
#define RC_OK 0X00
#define RC_ERR_UOP 0x01 // Unknown op code received
#define RC_ERR_MDATA 0x02 // Missing expected data packets
#define RC_ERR_OP_WDATA 0x03 // Wrong number of data packets for op
#define RC_ERR_INV_METR 0x04 // Invalid meter or gauge specified

const byte gauge_lookup_tbl[6] = GAUGE_LOOKUP;

int data = 2;
int clock = 3;
int latch = 4;
int debug = 0;

void setup() {
  int var = 0;
  byte spi_config = 0;

  Serial.begin(115200);
  pinMode(MLX_RESET_PIN, OUTPUT);
  pinMode(MLX_ERRB_PIN, INPUT);
  pinMode(data, OUTPUT);
  pinMode(clock, OUTPUT);
  pinMode(latch, OUTPUT);

  var = digitalRead(MLX_ERRB_PIN);
  digitalWrite(MLX_RESET_PIN, HIGH);
  delayMicroseconds(8000);
  SPSR &= B11111110; // 0th bit is SPIX2
  spi_config |= (1 << SPE) | (1 << MSTR) | (1 << SPR0);
  Spi.mode(spi_config);
}

void loop() {
  byte cmd = 0, dataPackets = 0, data[3];
  int rc = RC_OK, val = 0, gaugeNum = 0;

  data[0] = 0; data[1] = 0; data[2] = 0;

  if (Serial.available()) {
   cmd = Serial.read();
   updateLEDs(cmd);
   if (cmd == -1) return; // If nothing read no need to continue
   dataPackets = (cmd >> 3) & 0x3;
   switch(cmd >> 5) {
   case OP_SET_GAUGE:
   gaugeNum = cmd & 0x3;
   if (dataPackets != 2)
   rc = RC_ERR_OP_WDATA;
   else if (gaugeNum < 1 || gaugeNum > 5)
   rc = RC_ERR_INV_METR;
   else {
   rc = readDataBytes(data, dataPackets);
   if (rc == RC_OK) {
   val = data[0] << 8 | data[1];
   setGauge(gaugeNum, val);
   }
   }
   // TODO: Check pin ERRB on melexis to detect errors and return them
   //sendAck(RC_OK);
   break;
   case OP_ZERO_GAUGE:
   gaugeNum = cmd & 0x3;
   if (dataPackets != 0)
   rc = RC_ERR_OP_WDATA;
   else if (gaugeNum < 1 || gaugeNum > 5)
   rc = RC_ERR_INV_METR;
   else
   initMainLogometers();
   break;
   case OP_R_U_THERE:
   if (dataPackets != 0)
   rc = RC_ERR_OP_WDATA;
   break;
   case OP_DEBUG:
   debug = 1;
   if (dataPackets != 0)
   rc = RC_ERR_OP_WDATA;
   break;
   default:
   rc = RC_ERR_UOP;
   break;
   }
   sendAck(rc);
  }

}

int readDataBytes(byte *data, int count) {
  int i = 0, readCount = 0;
  byte cmd;

  for (i = 0; i < count; i++) {
   do {
   data = Serial.read();
   readCount++;
   if (data == -1)
   delayMicroseconds(SER_READ_DELAY);
   else
   break;
   } while (readCount < 10);
   if (data == -1)
   return RC_ERR_MDATA;
  }
  return RC_OK;
}

void sendAck(int errCode) {
  byte cmd = 0;

  cmd = ACK_CODE_BIT | (errCode & 0x7f);
  Serial.write(cmd);
}

void setGauge(int gauge, int val) {
  int quad = 0, offset = 0;

  quad = 0x3 & (3 + (val/512));
  offset = val % 512;
  sendByComp(gauge, quad, offset);
}

void initMainLogometers () {
  int i = 0, calDelay = 1000, quad = 0, offset = 0;
  for (i = 200; i < 1500; i += 4) {
   delayMicroseconds(calDelay);
   quad = 0x3 & (3 + (i/512));
   offset = i % 512;
   sendByComp(1, quad, offset);
   sendByComp(2, quad, offset);
  }
  for (i = 1500; i >= 200; i -= 4) {
   delayMicroseconds(calDelay);
   quad = 0x3 & (3 + (i/512));
   offset = i % 512;
   sendByComp(1, quad, offset);
   sendByComp(2, quad, offset);
  }
}

void sweepMainLogometers () {
  int i = 0, j = 0, calDelay = 2000;
  for (j = 3; j < 7; j++) {
   for (i = 0; i < 512; i++) {
   delayMicroseconds(calDelay);
   sendByComp(1, 0x3&j, i);
   sendByComp(2, 0x3&j, i);
   }
  }
  for (j = 6; j >= 3; j--) {
   for (i = 511; i >= 0; i--) {
   delayMicroseconds(calDelay);
   sendByComp(1, 0x3&j, i);
   sendByComp(2, 0x3&j, i);
   }
  }
}

void sendByComp(int gauge, int quad, int val) {
  byte b1;
  byte b2;

  if (val < 0 || val > 511) {
   pDataValidationError("Error valid quadrant table lookups are 0 to 511, received ", val);
   return;
  }

  if (quad < 0 || quad > 3) {
   pDataValidationError("Error valid quadrants are 0 to 3, received ", quad);
   return;
  }

  b1 = MLX_START_BIT | gauge_lookup_tbl[gauge] | (val >> 5);
  b2 = 0x00 | val << 3 | quad;

  digitalWrite(SS_PIN, HIGH);
  Spi.transfer(b1);
  Spi.transfer(b2);
  digitalWrite(SS_PIN, LOW);
}

void pDataValidationError(char *msg, int val) {
  Serial.print(msg);
  Serial.print(val);
  Serial.println();
}

void updateLEDs(int value){
  digitalWrite(latch, LOW); //Pulls the chips latch low
  shiftOut(data, clock, MSBFIRST, value); //Shifts out the 8 bits to the shift register
  digitalWrite(latch, HIGH); //Pulls the latch high displaying the data
}