We have install AIS Transponder FA-50. But I cannot switch it to Normal Mode in Silent menu. If I choose Normal mode, it always return to Silent mode all the same. Any suggestions?

I would recommend checking the silent mode wires (explained on page 1-10 of the manual) to ensure that they are not touching anything or each other.
I am having the same issue and the silent mode wires are not touching anything.... Any ideas?
Where are the dip switches located on the FA-50?

Also, the only light on is the green power. I am receiving AIS targets but am not transmitting.
Found the DIP switches. 1-4 are all in the same position and set to the right if looking at the unit from the front.
If this is a new install, the boat name and MMSI must be setup/configured or the unit will not transmit. The included GPS antenna (GPA017) MUST be working and connected for the unit to transmit. The whip antenna MUST be suitable for AIS and not a basic VHF antenna for the unit to transmit. If you are receiving, you should get an RX light (yellow) flashing from time to time. If you watch the TX light, it will flash (depending on your speed) at least every 3 mins. It will be BLUE if it is good, and yellow if there is a problem.

I will be out of pocket for a few weeks so if you continue to have problems, you might want to open an official support case.
This is a new install. The MMSI and user data has been setup using the furonservice and FA50 password. GPS antenna is connected and tested out. Shakespeare 5250-AIS whip antenna is connected.

I think I just saw a blue light flash. How do I know it is transmitting. Under the setup from the MFD12 it will not let me select off of silent.

Does the vessel need to be underway to transmit?
The software selection for silent mode shouldn't be messed with; and it really won't do anything, unless a hardware jumper has be placed on the board. The normal way to go into silent mode is with a toggle switch using the dedicated Purple and Gray wires. (shown on page S1 of the interconnection diagram).

IF you were in silent mode, the transmit light would be yellow not blue.
It may be a stupid question but where exactly do I connect the silent switch to grey/purple wires? I looked at the diagram, thought it would be supereasy, but when I popped the unit cover off I just could not find what I was looking for. :questions
Your power cable, of the FA-50unit, has other wires including the ones you are looking for. If you don't find the wires, then you might have an older FA-50 unit prior to this option being added.