I upgraded the motherboard's firmware to the latest I could see for this model - F5.
The HBA's BIOS and firmware were upgraded using a different system (they were dated early 2011). This did no change in regard for getting the card to be recognized on the newer Z77 motherboard. I also tried clearing the CMOS settings on the Z77 motherboard, but no help.
On the older G45 mobo I get the SAS/SATA HBA's BIOS prompt after POST just before the OS loads, where I'm able to configure the card/disks/arrays, but on the Z77 this prompt is never shown.
Device manager doesn't show this device but I can well understand why.