There is probably a setting in the Promise Card's BIOS to make your machine boot from it. Also, you will probably have to reinstall your operating system, telling it about the controller card when you enter the blue text based stage. You may be able to rescue your current installation using rescue mode and the drivers disk, but I doubt it.
You would certainly be going into your motherboard's BIOS as well, I guess, and disabling anything that tries to boot from the onboard controllers, since you now only have optical devices connected to those.
So, really I think there are changes in the machine's BIOS and in the card's BIOS as well. If the card is so cheap that it does not have one, then basically it does not have a boot rom, and you can't boot from it, only attach drives to it.
One solution in this case would be to keep your OS drive on the motherboard and only attach your second drive to it, since its not likely you will be booting from this other drive ever. You'd be able to keep your 3 optical drives because there would still be primary slave, secondary master and secondary slave available for those on the on-board controllers. You would then attach any additional hard drives to the card.
Onboard IDE
P/M - Operating system HDD
P/S - Optical Drive
S/M - Optical Drive
S/S - Optical Drive
Controller Card IDE
-2nd HDD
-Any additional HDDs.
I assume you would not want more than 3 optical drives (I never managed to keep more than 3 then I was in the period of wanting multiple optical drives in my machine) and you leave the possibility of adding 3 other HDDs in the future for additional storage. (I am assuming a 4 HDD capable card here, yours maybe only supports 2 drive.)
When you start to create bigger and more powerful machines that have multiple optical drives and multiple hard drives and / or RAID arrays, these are the very sorts of issues you will run into often, and you just have to try to think of ways to accomodate them.