WAS A 6 SPEED MANUAL AVAILABLE ON THE 2004 BASE MODEL

I think it was just a 5speed manual for the base model coopers.

5-speed Midlands for '02 through '04. Later 1st generation cars had 5-speed Getrag. Not sure if the changeover coincided perfectly with the model-year '05 refresh. Current Cooper and Cooper S coupes use 6-speed Getrag, but with different gear ratios depending on model.

Chris is correct. The Midland trannies were poorly designed as well. Lots of issues. If your car is stock, you'll want the '05-'06 tranny. If you plan to build a fast MINI (where you're going to be flying through the gears), the '02-'04 trannies are better in my opinion (1st gear is just a tad bit longer).

Can I change my 03 over to a six speed by simply changing the transmission out

I want to install a 6 speed S model manual transmission in my 2004 base model. Can I remove and replace or is it a major problem?