Here's what the Codes are for...... 030 isn't the engine BTW, it's the Monitor System. 113 is the Power Train Control which is more likely to be interesting in the diagnosis of this particular problem.
030 096F03 - Fuel Level Sensor, Voltage Above Normal.
030 819F02 - Monitor Display Datalink, Data Erratic, Intermittent, or Incorrect.
030 821F04 - Monitor Display Power Supply, Voltage Below Normal.
113 070F02 - Parking Brake Switch, Data Erratic, Intermittent, or Incorrect.
113 168F03 - System Voltage, Voltage Above Normal.
113 168F04 - System Voltage, Voltage Below Normal.
113 177F03 - Trans Oil Temp Sensor, Voltage Above Normal.
113 298F02 - Service Brake Pedal Switch, Data Erratic, Intermittent, or Incorrect. (As I asked before. Are you sure that the switch is connected correctly..?)
113 299F13 - Transmission Lever Position Sensor, Requires Calibration
113 468F08 - Service Brake Pedal Position Sensor, Abnormal Frequency, Pulse width, or Period. I did mention this was a PWM sensor didn't I..?
113 623F02 - Directional (Reverse) Switch, Data Erratic, Intermittent, or Incorrect. This is not the same as the Transmission Lever. It's a switch similar to the one on the service Brake pedal.
113 671F02 - Transmission Output Speed Sensor, Data Erratic, Intermittent, or Incorrect.
All the suspects for causing the problem with your tractor are there in that list. Park Brk Switch, Service Brk Pedal Sensor & Switch, Transmission Control, & Directional/Reverse Switch.
As Mark & I both suggested, try erasing the codes as per the instructions at the end of Page 2. Once you have them all erased try powering up the machine again, fire up the engine and try to move the machine and see what happens. Observe carefully at what point the SERV CODE icon lights up. I'm sure some Codes will return despite not being Active in your list. That will point us in the right direction.