Let's start by getting to a common set of terms. Primary and Secondary are not usually used to label disk drives.
A motherboard (mobo) might have either one or two IDE ports - the ones with 40 pins in a 2 x 20 arrangement. On the mobo and in the BIOS Setup screens they may be called IDE0 and IDE1, IDE Channel 0 and IDE Channel 1, or the Primary and Secondary IDE Channels. Some systems label them as ports 1 and 2, instead of 0 and 1. For EACH of those IDE ports it is possible to have up to two devices sharing the port and data ribbon cable, and they are called the Master and Slave devices on that port. So, you can have a Primary IDE Master, a Primary IDE Slave, a Secondary IDE Master, and a Secondary IDE Slave. How many IDE devices do you have, and how are they connected to how many IDE ports? You seem to indicate that you have two IDE hard drives, but maybe you have other devices like optical drives on the IDE ports, too.
The SATA ports are entirely separate from the IDE ports. In most cases (yes, there are some exceptions on older mobos) you can use any and all SATA ports IN ADDITION TO the IDE ports. There is no reason to disconnect an IDE device to "make room for" a SATA device on a different port. As I said in my previous post, the BIOS language can be confusing on this because some of them use terms like "IDE 3 Master" to label the only device on the first SATA port, even though that port on the mobo may have a label like "SATA 0".
In the BIOS Setup screens, in the places where the IDE and SATA ports are configured, there usually are places where you can Enable or Disable all the IDE ports at once, and all the SATA ports. Obviously your IDE ports are Enabled - you've been using them. But check whether your SATA port is Enabled, since you say the mobo fails to "recognize" it. However, it does seem VERY hard to understand how the mobo can NOT "see" that SATA drive and still let Windows use it normally.
What version of Windows are you using? If it is Win XP in any form, you might need to check a BIOS setting. If it is Vista or Win 7, not so important.
The setting I'm talking about is called the SATA Port Mode, and it is set in a line very near where you Enable the SATA Port. Win XP does not know how to use a SATA device (or more properly, an AHCI device) unless a driver is installed. For those who actually need to BOOT from a SATA drive into Win XP, there is a special procedure available OR there is a special feature in most BIOS's to solve this problem. For that situation you can set the SATA Port Mode to "IDE (or PATA) Emulation", and the BIOS will fool Windows into thinking it is using an IDE device it already understands. However, if you are NOT going to boot from the SATA unit in XP and use it only for data storage, you can set the Port Mode to AHCI and Windows can simply load the required driver for that after it has booted from another drive. In the cases of Vista and Win 7, all this is unnecessary - you set the Port Mode to AHCI and those versions of Windows DO have the required drivers "built in".
I'm not clear why you remove the second IDE drive when you want to connect a SATA drive. Do you believe they are incompatible? Are you running out of power connectors for drives? Do you not have enough mounting slots to put in more than two drives? There are solutions to all of these, so let us know.
By the way, what type of power input connector does your SATA drive have? IDE drives have a 4-pin connector called "Molex", and current SATA units have a very different 15-pin connector. But some early SATA drives had both on them to allow for early users whose Power Supply Units did not have the new SATA power output connectors. In those cases you had to connect power to ONE or those, not both. (The 7-pin data ribbon cable also is needed, of course.)