@ tntexplosivesltd : The general principle of the code would be to use PWMOUT to generate a 38kHz carrier signal, then connect the IR LED + R between the PWMOUT and an output pin which can turn the LED on and off to modulate it. The timing control is achieved by using PULSOUT to the LED pin to create a pulse of IR and a PULSOUT to an unused pin to create the gaps between pulses.
For example, this code should notionally generate ten pulses of 100us IR with 1ms gaps between them once every second ...
PwmOut PWM_PIN , 25, 53 ' 38kHz at 4MHz
Do
For b0 = 1 To 10
PulsOut LED_PIN, 10 ' 10 x 10us = 100us
PulsOut DUMMY, 100 ' 100 x 10us = 1000us = 1ms
Next
Pause 1000
Loop
That's only notional timing though because it doesn't take into account the time of instruction execution itself so you need an oscilloscope or logic analyser to fine tune it. If the timing isn't what the receiver expects the IR will simply be ignored.
Once you can generate IR signals, then it's a case of generating the required signals for each key press with the correct timings. If which keys generate which signals isn't known that has to be reverse engineered from looking at the signal from a remote controller known to work.
Then you've got to scan the keys and simply generate the correct codes. With a large memory PICAXE that may be a long list of subroutines for each code generated, with smaller memory you have to work out a way to build each sequence to send depending on key pressed.
The principle is simple but the doing it can be a long and involved exercise. I wouldn't attempt the project without access to an oscilloscope as it would be near impossible to get it to work by guesswork.