Thats just a BIT rusty mate. Are you sure you need replacements ?
The radio doesnt work because its code protected.
If you have the genuine log book of the MX5 that came with the car, you should find a little card in there that says "CODE", its for your radio.
However, make sure you dont input the wrong code. Every time you put the wrong code in, the radio will need more time to reset to where you input the code. On the 10th attempt it will lock permanently.
1st attempt will need for the radio to stay on for 5 mins to return to the input screen
2nd attempt will need 15 mins
3rd attempt 1 hour
4th attempt 4 hours
and so on....
If you turn the ignition off and the radio goes off, when you turn it back on, it starts counting the current attempt's time from the beginning.
What I usually do in these cases is put it on a battery on its own and have the battery on a small charger over night.