Electronic – arduino – IR Remote code for Arduino

You don't mention the word "protocol" in your question, but you must know that there's a number of protocols around, not everybody uses the same coding. That makes "full knowledge" a tall order. RC-5 Telaclavo refers to (as one of the most used) is totally different from the Sony SIRC protocol, for instance.

This page suggests Humax uses the NEC protocol:

"The Hex Code Generator for Yamaha is for NEC IR Protocol which is the same for Onkyo and many other manufacturers e.g. Toshiba,Humax etc."

Modulation is at 38kHz, not 36.

Details about the NEC protocol can be found here and here. The latter link also lists a few commands.

Building a replacement remote controller would be a silly idea; for a few dollar you can buy a universal, programmable RC.
If you really want to you'll need little more than a microcontroller. In the old days there were specific ICs for remote controls, the SAA3010 was the standard for RC-5, and was used in 100s of millions of remote controls. But today a microcontroller is as cheap. The program is easy: when you wake up on interrupt scan the keypad, and if a key is detected, send a serial datastream of the modulated code to the output. Repeat until the button is released and go to sleep.
There will be a transistor which drives the IR LED(s), and that's it. Most of the time a series resistor for the LEDs isn't even used.

further reading
Using the Philips 87LPC76x microcontroller as a remote control transmitter, NXP application note for an RC-5 remote controller.

A simple way to debug would be to use an oscilloscpe to compare the difference between the real remote and your Arduino signal.

Either use an IR receiver and scope the results of both Arduino and remote with the same data sent. Or open the remote and scope the lines directly and compare with the Arduino data driving lines. Then adjust your code to make the two identical. As @mpflaga says, the timing between sends is a likely suspect.