So... my report back...
The 740i (E38) Climate Control unit is somewhat different to the 328i, nevertheless...
I removed the unit pretty easily once I realised that I needed to remove a cover to the right of the cup holder by simply pushing up on a clip and gently nudging it forward.
In other words, under the climate control, you have a dual cup holder... To the right of that, is a small cover about two inches long and one inch high. Simply stick your finger underneath that and you will find a clip that you will have to push up on and at the same time gently nudge the cover forward.
It will pop out and you will now be able to stick your finger through the hole - upwards. You will easily be able to gently push the climate control unit out. (No tools were used at all)
I then disconnected all the wires - beautiful clips
made it really a simply procedure. There were 5 clips in total.
Once on my desk, I easily removed the outer shell to reveal the pcb board.
On the board, I found three caps that looked similar to the unit from the 328i, but managed to find the .47uF cap with the help of a standard voltage tester.
After changing the cap and putting the unit back together, I am happy to report that it worked!
My climate control is good as new and in less that 30 minutes!
Total cost of repair = ZAR17-00 including the electricity needed for the soldering iron
Converted into US Dollar it works out at around $2-42
Thank you Stevo and the Bimmer forums!