BIOS EPROMS on add-in cards work as extensions to the motherboard BIOS, they do not replace it and would not be seen at all without the motherboard BIOS working correctly.
eg. If you get an older IDE / ATAPI adapter card that has an on-board EPROM, the motherboard BIOS should detect it and automatically use it for the functions of the IDE card.
Likewise a network card - the EPROM on that just allows the main BIOS to boot from a different data source, rather than a local drive.
However; if having the drive connected means the startup / BIOS screens are not appearing, either the cable is mis-connected or the motherboard BIOS simply cannot communicate with the SSD.
If it's not trying to start, you cannot use that SSD on that connection, no matter what else you do.
If it's still not working with the SSD disconnected from the motherboard, some other connections have been disturbed or there is a fault somewhere with the PSU / Motherboard / CPU / RAM.
If you have a speaker connected directly to the motherboard, does it give beep codes? That indicates it's trying but detecting a problem
If you do not get anything, an IDE (or other) connector is in backwards or something has probably failed.