Alfie,
Lovely yacht, and an excellent reason to get her back on the water
The person who did the installation was very organised and efficient, and the good news is that the servos are just right already
I think that the transmitter (the bit in your second picture) is a Flight Link (from the colour) and if the battery corrosion can be fixed it is easy to buy new rechargable cells, and also the charger for them
In the boat the white box on the left contains the 27 Mhz receiver and a switch for 4 crystals (and the names tell us it is 27MHz)
So if the radio can be got working you can go sailing directly - 27 is legal for any model
I have NO IDEA what the printed circuit board beside the rudder servo is - possibly a throw adjuster for the sailwinch servo?
In an ideal world I would suggest getting someone familiar with R/c to give it an eyeball - they would be able to test each component and mimimise expenditure
How about finding a local yacht-sailing club and taking it along?
In an ideal world I would suggest replacing the 27 MHZ radio equipment with 2.4 GHZ - specifically a Planet 5, which in my opinion is the most economic (non-toy) radio and batteries to suit, and
ENJOY
andrew